The 1940 census is now available on the computers at the library! (Once you get here and log on, click on Ancestry, then 1940 U.S. Census). The 1940 census is still in beta, so you can only search by name for people who lived in Delaware and Nevada. However, on the right side of the page is a browse tool that lets you select a state, county and town.
If you select New Jersey, Union County and New Providence (Berkeley Heights' original name), you have a choice of census enumeration districts. The census enumeration districts for New Providence Township are 20-62A, 20-62B, and 20-63. These districts are described geographically to help you figure out which one you need. Because you can't search these by name yet, you'll have 38, 18 or 11 pages to browse through looking for that relative of yours in Berkeley Heights. We'll keep you posted once the entire 1940 census can be searched by name.
The censuses after 1940 are not available. To protect the privacy of individuals, the census bureau will not release them until 72 years have gone by.