Garageband is good. Audacity is also good for audio editing. Here's my greatly simplified process:
1) Add a metronome to the song in a separate track in Audacity using "Generate -> Click Track...", simply making educated guesses at the tempo until I find it.
2) Export that with a mix of song and click that I like to an .mp3 for easy practice.
3) Record both audio and video of the cover while playing along to the metronome version.
4) Add my audio to the original project as a new track, lining it up where my performance sounds its best against the original drums.
5) Mute the click track, and mix and export this audio, so I have a final audio file with both the song and my drums in it.
6) Sync the audio and the video in the video editor and export that.
Very simplified but that's the workflow for me.