Construction laborers, Riverside Park, May 16, 1934. Photo: New York City Department of Parks and Recreation:

Prior to the New Deal, the New York Central Railroad ran along the Hudson River on the west side of Manhattan, not only cutting residents off from the river, but also spewing coal smoke and soot into the residential areas. A project was launched in 1929 to bury the railroad tracks under parkland but it never got off the ground due to lack of funding, and by 1934 what we know as Riverside Park today was a "wasteland ..." stretching from 72nd Street to 181st Street ... "a vast low-lying mass of dirt of and mud ... unpainted, rusting, jagged wire fences along the tracks barred the city from its waterfront; in the whole six miles, there were exactly three bridges on which the tracks could be crossed, and they led only to private boating clubs ... [a] stench [hung] over Riverside Drive endlessly after each passage of a train carrying south to the slaughterhouses ... carload after carload of cattle and pigs..."[1, pp. 65-67] 

Riverside Park Hooverville, 1933. Click to enlarge.

Plus "fifty-two shacks comprising the veterans' camp between 72nd and 79th Street ... [and] eighty-three other shacks along Riverside Drive on the Hudson River ... [plus] a reinforced coal hopper at the foot of 96th Street... [plus] old docks [plus] eleven shacks built around the piling tinder [at] the dock at 96th Street ... these wharf dwellers are literally clinging to the underpinnings of the rotting dock structure"[2].

”The fifty-two shacks comprising the veterans' camp between 72nd Street and 79th Street, between Riverside Drive and the Hudson River [inset photo] will be torn down on May the first. Provision has been made for the Department of Public Welfare to transfer these men to a farm at Greycourt. There are eighty-three other shacks along Riverside Drive on the Hudson River, housing over one hundred men, which will be torn down at the same time that the Hudson River Yacht Club and the Columbia Yacht Club will be demolished.”[7]

West Side Improvement 1937. Photo: NYC Parks Department Archive. Click to enlarge.

In 1934 Robert Moses launched the West Side Improvement Project to create from this a mess a 5½-mile-long park, an express highway, and two boat basins. He obtained funding from “many sources ... Governor Lehman approved a loan of grade-crossing-elimination money to the New York Central. Federal, state, and City grade-crossing moneys, City street and park funds raised by assessment, railroad funds, money obtained through the sale of bonds of a municipal authority, Federal and state highway money and relief funds were also included.”[3] Moses is (as always) deliberately vague about the funding, and doesn't even mention the labor. But this was a massive work project and Moses commanded an army of as many as 80,000 relief workers during this period: if they didn't build it, who did?

Robert Caro, as usual, to the rescue [1]:  Moses calculated that he had to find $109 million for the project, and Caro recounts how he did it; it's the kind of feat only Moses could pull off and Caro's pages are worth a read if you want to make your head spin. But to summarize (and perhaps oversimplify very slightly 14 pages of twists and turns), Moses received (in round numbers) $42M for the project from the Federal government ($30M from the PWA and CWA, $12M from federal interstate highway funds), $23M from the City and State, and $3M from private sources (this adds up to $68M, considerably short of his original estimate for reasons explained in Caro: cutbacks, sleight of hand, etc).

Today Riverside and Fort Washington Parks are an essential fixture of Manhattan's West Side. They include not only parkland, but a mall overlooking the Hudson River; baseball, football, and soccer fields, playgrounds, sprinklers, wading pools, running tracks, volleyball courts, tennis courts, bicycle paths, skate parks, and boat basins. It's really one big long park from 72nd Street to 181st Street, but there is an invisible boundary at 155th Street with Riverside Park to the south and Fort Washington Park to the north.

References:

1. Caro, Robert A., The Power Broker - Robert Moses and the Fall of New York, Vintage Books (1974), pp.526-540. According to Caro, Moses obtained $13.5M from NY Central (which NY Central obtained from the State), $12M from federal interstate highway funds, $10M from a city tax levied on Riverside Drive property owners, $1.766M from PWA for materials to build the 79th Street Boat Basin, $3M from the CWA for labor on the Boat Basin, another $20M from the CWA for materials and equipment for the rest of the park up to 192nd Street, another $5M in labor from the CWA for the park and highway north of 192nd Street, and finally by sale of $3M in Henry Hudson Parkway Authority bonds to the banks. So of the $58M that Moses raised for the project, $42M came directly from the federal government, $23M came from the City and State, and only $3M (4%) came from private sources via bond sales to banks.
2. NYC Parks Dept press release of April 27, 1934, announcing commencement of work on the extension of Riverside Park along the west side of the New York Central Railroad tracks as part of the West Side Improvement Project using relief labor: Demolition of squatter shacks, coal hoppers, old docks.
3. Moses, Robert, Public Works, McGraw Hill (1970), p.183-188.
4. NYC Parks Dept press release archive for July-December 1934: numerous documents regarding the Columbia University Yacht Club in Riverside Park, which Moses demolished.
5. The Columbia Yacht Club (gallery), Tours by Gary at blogspot.com.
6. NYC Parks Dept press release of July 31, 1934, "West Side Improvement", the first phase of the construction of Riverside Park, which states that after the retaining walls for the railroad are built, "it will be possible to proceed with the landscaping work wilth relief labor."
7. NYC Parks Dept press release of October 29, 1934, Memorandum on Organization of Work Relief Projects: “The relief workers in the parks had been recruited through the National Reemploymont Service and passed through the Civil Works Administration to the various city departments. The Park Department inherited 69,000 of them.”
8. NYC Parks Dept press release of February 27, 1935: The beginning of work on the extension of Riverside Park along the west side of the New York Central Railroad tracks. “Dirt and rock fill is being brought into the area north of 72nd Street at the rate of 500 truck loads a day ... The areas not occupied by the highway will be landscaped and utilized·for various park activities. At 79th Street, which will be carried down to the waterfront by means of a grade crossing elimination, there will be a boat basin, and just to the south a large swimming bowl is planned. At 96th Street there will bo a second grade crossing elimination. A total of 1,000,000 cubic yards of fill is required to reclaim the entire area. Of this amount 800,000 cubic yards will come from the railroad cut under construction by the New York Central from 42nd to 64th Streets. Two contracts already have been let calling for delivery of 400,000 cubic yards during the next four months at the rate of 4,000 cubic yards a day. All the stone taken from the cut will be used to construct a rip-rap wall along the park waterfront. Work on this wall is expected to begin shortly. Relief labor will be used entirely. A squad of relief workers aided by several cranes and 'bull dozers' (grading machines) already are at work on the dirt now coming in.”
9. NYC Parks Dept press release of January 10, 1936: ”The Board of Estimate and Apportionment has received the Department of Parks' plans and specifications and estimates of cost for the covering of the New York Central Railroad tracks, continuation of the West Side Highway and park restoration through the entire length of Riverside Park ... The plan calls for the complete covering of the New York Central Railroad tracks through Riverside Park and the covering is used for promenades and overlooks banked by trees and landscaping.”
10. NYC Parks Dept press release of October 3, 1937: “The Department of Parks announces that on Tuesday, October 12th, the 6.7 miles of parkway now under construction in Riverside and Fort Washington Parks in connection with the West Side Improvement will be officially opened to the public, thereby adding another vital link in a great arterial express highway and parkway system for the City of New York. Besides the parkway there will also be available for public use, 78 acres of play area including children's playgrounds, athletic fields and tennis courts. The entire area west of the railroad at Inwood Hill Park extending from Dyckman Street to the Harlem Ship Canal, will be devoted exclusively to active recreation. Promenades and winding foot paths with benches under shade trees will be available for pedestrians and those seeking rest and quiet. Plans have also been developed for marine recreational facilities in the form of four boat basins located respectively at 79th Street, 96th Street, 148th Street and Dyckman Street. All but the 148th Street basin which will be under the jurisdiction of the Commissioner of Docks, will be operated by the Department of Parks. The basins at 79th and 96th Streets are actually under construction.” If the 96th Street and 148th Street boat basins were ever constructed, there is no trace of them now. “The opening of the West Side Improvement through Riverside and Fort Washington Parks from 72nd to Dyckman Streets will provide at a total cost of $24,340,000., an immediate usable section of a great marginal waterfront development. 132 acres of new park land valued at $30,000,000., have been made by filling land under water and covering of the railroad tracks. Approximately 3,000,000 cubic yards of fill from exterior sources have been used.”
11. NYC Parks Dept press release of October 11, 1937, announcing the opening of the West Side Improvement in Riverside and Fort Washington Parks, a $24,340,000 project.
12. Interesting Places in the Parks of New York City, undated document in the October section of the 1937 Parks Department press release archive: “WEST SIDE IMPROVEMENT - The plan for the West Side Improvement along Riverside Drive from 72nd Street to Dyckman Street includes a wide variety of facilities for active recreation, When this work is completed, there will be eight children's playgrounds with wading pools and recreational buildings; twelve full-size baseball fields and seven soft ball diamonds. A miniature Randall's Island track and field layout will be a feature. Thirty handball, twenty horseshoe and fifteen tennis courts, plus a large number of shuffle boards, basket ball, paddle tennis and other court games are being constructed. Three new boat basins will be built for motor boat fans; bicyclists will have an exclusive river front track, while roller skating enthusiasts will have eighteen city blocks of track and two roller hockey rinks.
13. NYC Parks Dept press release of March 2, 1940, announcing the opening of the 79th Street Boat Basin.
14. Riverside Park Construction 1934-37 (gallery), New York City Department of Records at nycma.lunaimaging.com.
15. Klein, Milton M., The Empire State: A History of New York, Cornell University Press (2005). "...and [Moses] strung together federal and state grants for New York State's largest public work, the $205 million West Side Improvement which extended Riverside Park over the New York Central Tracks and built the Henry Hudson Parkway to connect with the Saw Mill River Parkway." (Obviously there were cost overruns after his original $109 million estimate.)
16. New York City Parks Department press release, December 1938: Progress in the Park Department: 1934-1938.
17. New York City Parks Department press release, August 11, 1939, New Police Precinct for Riverside Park.
18. New York City Parks Department press release, June 23, 1939: Opening of recreation areas in Riverside and Inwood Hill Parks, 145th-155th Streets and from Dyckman Street north to the top of Manhattan (previously a dump), with ceremonies in which Robert Moses and Alexander MacGregor, Assistant to the Works Progress Administrator, participated. “The work was planned by the Park Department and performed by the Works Progress Administration.”
19. New York City Parks Department press release, November 30, 1939, A million tulips planted in Riverside Park and along Henry Hudson Parkway.
20. Federal Writers' Project, The WPA Guide to New York City, Random House (1939), pp.284-289.
21. New York City Parks Department press release, July 15, 1941, Hudson River overlook at 149-150 Street “which was built by the Works Projects Administration”.