I’m curious about this. Once I tried to import a song to GarageBand, but when I went to set the tempo, I found the the original recording varied in tempo quite a bit, so it was constantly moving ahead/falling behind the metronome. Sounds like this is a way to overcome that problem?
I first use this online tool to measure the tempo of the song. Then I come back to Ableton, choose “Warp” (you can see in the image), and set the BPM.
Ableton is often smart enough to automatically mark drum beats (little light gray dots you see on top of the waveform). If it is an electronic music piece, or if the original was recorded with a metronome, these will automatically be perfectly on the beat.
If it is not, then I reduce the main BPM to slow down the audio. Then I listen carefully to understand which of these drum beats are supposed to be on the beat and drag & drop them to the perfect location. In the image, you can see 2 examples (the orange markers on the waveform). These markers were like other small gray markers and I dragged them to their correct location.
Doing this for a few beats during the song aligns the rest of it. Some older songs are all over the place, for them, I mark almost every bar. For blues songs, I usually mark every 12 bars.
Hope this makes sense. Happy to answer any more questions.