Music- time signitures Watch
First work out when the beat of the music is and tap along in your head
Then work out how many of those beats are in a bar, by listening to whether the beats are grouped in 2's, 3's, 4's etc. (they're the most common ones). To practice this listen to a waltz (3 beats in a bar) and a march (2 beats in a bar) to get an understanding of the difference.
Then, to work out if it is simple or compound time, listen to whether each beat is divided itself into triplets (3's) or duples (2's) . If it's triplets, then it's compound time and if it's duple, then it's simple time (most common). To practice this, listen to a Gigue (compound time) and a Gavotte (simple time) - there'll be loads on youtube.
With these two bits of information, you can now work out the time signature.
If it's simple time, then the time signatures will be (in almost all listening exam cases):
2/4, 3/4, 4/4, 5/4 etc. whereby the first number refers to how many beats are in a bar (how they are grouped in the piece).
If it's compound time, then the time signatures will be:
6/8, 9/8, 12/8 whereby the first number refers to 3x the number of beats in a bar (i.e if there's 2 beats in a bar, it's 6/8, 3 beats 9/8, 4 beats 12/8 etc.).
There are other time signatures but even to the trained ear, it's very hard to distinguish between 2/2 and 2/4 for example. However 2/2 is quite unusual and no listening exam would test you on this. Also, very often, if you mix up 2/4 and 4/4 they will still award you the marks as they sound quite similar.
Hope this helps!