This is a tough one, at least in order to do it legally. In order to perform a song legally or even playback a recording publicly you need to license it and/or pay royalties to whomever owns the copyright on that song. Everywhere you hear music - television, radio, professional stage shows, even in an office building - they pay some sort of fees. The exceptions are songs that are in the public domain - generally anything written before 1923 - and songs that are licensed under Creative Commons.
Virtually all commercial music is copyrighted and subject to licensing fees unless you know the artist and can get their permission. Many common, popular songs like "Happy Birthday" that you might think are public domain are actually protected by copyright.
If you are posting videos to YouTube, some music publishers have deals with YouTube that allow users to upload videos that contain their music, BUT the catch is that the music publisher can have YouTube remove your content at any time, for any reason.
"Jingle Bells" is in the public domain (I think it was written in the 19th century by James Pierpont). You could try downloading a MIDI file of it and then using a program like Garage Band to put together a decent, original version of it. There are a lot of decent MIDI tracks you can use to make music, but it's important to check the copyright on each song to make sure it's OK to use.