A warning first: finding the sequence of time signatures in a song by ear can be maddeningly imprecise at times. You can't figure out with 100% certainty whether a song has /4, /8, or even /16 at the bottom of its time signature, you can't completely determine whether a song is in 4/4, 2/2, or 2/4 time, you'll probably end up wondering whether a song is in 3/4 or a slow 6/8 at some point...
But you can still find a sequence of time signatures that most listeners will accept.
For more straightforward mixed meter examples (e.g. Golden Sun boss themes--the Doom Dragon theme is a good example), merely finding the most strongly accented beats and treating them as the starts of new measures should be good enough. I generally treat the music as if its fastest notes are 16th notes, which should help when determining the meter.
For stuff involving polyrhythms, I'd say that the meter that involves the most instruments wins (e.g. if the piece involves triplets over septuplets, but 2 instruments are playing triplets and 1 is playing septuplets, I'd rather say that the piece is in triple meter). If there's a tie, I'd say the drums are the tiebreaker (although things get even tougher if the drums are also playing polyrhythms). A caveat: it's your call whether you say the meter of the piece reflects the "most popular tuplet" or some overarching tuplet pattern (e.g. if said triplets-over-septuplets piece consistently puts them in groups of 4, then you might be able to say that the piece is in 4/4 with lots of tuplets).
And then you'll have to take tempo changes into account. When a tempo change and a meter change occur at the same time, that's when things get really aggravating.