I complement @user6726's answer with two more pieces of information.
Was the song published before 1922?
Anything published after 1922, such as the popular Wheels on the bus which is on that list, may be under automatic copyright in the US and may not be worth finding evidence for. This post calls the "Mickey Mouse curve":
In 1976, Congress authorized a major overhaul of the copyright system assuring Disney extended protection. Instead of the maximum of 56 years with extensions, individual authors were granted protection for their life plus an additional 50 years, (which was the norm in Europe). For works authored by corporations, the 1976 legislation also granted a retroactive extension for works published before the new system took effect. The maximum term for already-published works was lengthened from 56 years to 75 years pushing Mickey protection out to 2003. Anything published in 1922 or before was in the public domain. Anything after that may still be under copyright.
Even then, it's a grey area, for example the melody of "Wheels on the bus" is from "Here we go round the mulberry bush", which is in the public domain (see the point below and this post).
Is the song on this list?
This list of children songs in the public domain is a reasonable indication that a song is in the public domain in the USA, though to be sure, you would need to order the reprint and confirm the melody:
This list is based on USA Copyright Law and is intended only as a help in researching public domain music. This list is NOT sufficient documentation that music is in the Public Domain. To prove PD status in the USA, you MUST find a published copy of the song with a copyright date of 1924 or earlier. Our PD Sheet Music Reprints are exact reprints of books and sheet music published in 1924 or earlier and include music, lyrics, and complete original copyright information. Some of these songs may not be PD in countries other than the USA.