With regard to the conductor, look for the downbeat (it looks exactly like what it says on the box), then count the number of beats that occur in between before the next down beat happens, and that will give you the count. Downbeat + 3 more beats and a new downbeat, gives you a time signature in fours. (When listening, just the same principle, but now its the most heavily accented beat you hear that carries the downbeat, the rest of the process is the same.) Working out whether the actual time signature is 4/4, 4/8 or 4/2 takes a little more experience as it will be the character of the piece as a whole that gives the game away. E.g. something with 6 beats, chugging along in 2 groups of 3, a bit like a jig or gigue, is likely to be in 6/8 time, but it could of course be in 2/4 in triplet 8ths too. Experience of the different forms and their characteristics will nudge you to resolve it one way or the other, together with a sharp ear for the relative weights of those (weaker) beats other than the main ones, e.g. are those 6 beats I mentioned before actually grouped as 3 x 2, or 2 x 3, or other crafty tricks like Tchaikovsky's famous knack of making 5/4 sound uncannily like a (mildly deranged) waltz in 3/4. :-)
The principle remains the same though: establish the down beat, work out where the next one comes, and then work backwards to establish the count. And keep listening and (if needs be) keep (re-)evaluating what is actually happening in time: time signatures can and *do* change in mid-flight..! :-)