Image: Young woman playing guitar and singing with friends. (bbernard/Shutterstock, all rights reserved.)
Zemirot (singular is z’mirah) are Jewish songs with an association with Shabbat or holidays. Many zemirot are sung to several different tunes, and for the most popular, new tunes are being written all the time. Some Sephardic Jews also use the term to refer to the series of psalms in the morning service prior to the Barechu prayer.
The Zemirot Database is an online collection of zemirot with lyrics in the original language (Hebrew, Yiddish, Ladino, etc), and a translation into English. It also lists information about the origins of the song and links to recordings.
Another place to find zemirot is on YouTube.com. If you know the title (often the first few words of the song) you can search and find recordings on YouTube.
Some zemirot that may be familiar as Shabbat table songs:
Another way to learn zemirot, the best way, is to learn with a bunch of Jews singing them together – learn around a Shabbat table, or at services at your synagogue.