Hugh, I’m only answering you because of your sig, and because it was on my mind today. Just so you know. A time signature is the number of beats in a measure (which probably doesn’t help you at all).
Listen for a moment to any standard rock and roll song. Just turn on the radio, really. Wait for all the commercials to end. Good, now tap your foot to the beat. Now that you’re tapping, pay attention. Are you unconsciously tapping harder once every two or four beats? Is there a rhythm (particularly in the percussion) that repeats very frequently, like every second or two? Listen for the bass drum, perhaps. That’s a good way to figure out, without looking at the sheet music, how long a measure is.
Now count the beats in a measure. You might say there’s two, your friend might say four, another really hyper friend might say eight. Doesn’t really matter: the piece is most likely in “4/4 time” (spoken: “four four time” or “four quarter time” or “common time”). That means there are four quarter-notes in each measure. The top number is relevant if you’re listening to a song or dancing to it; the bottom number (and the meaning of a quarter note) is largely irrelevant unless you’re performing the song.
Waltzes (like the Blue Danube or REM’s Everybody Hurts) are said to be in “3/4 time” (spoken: “three quarter time” or “waltz time”). It’s tricky, though: without seeing the sheet music, you can’t really tell what the song is written in. The best you can do is say “oh, that’s in three,” and a musician might say “Hm, it sounds more like six,” and you nod appreciatively and say “I guess it could be.” “Everybody Hurts,” now that I think of it, sounds more like six. It has to do with how often the pattern repeats, but I don’t have a foolproof way to tell just by listening.
Dave Brubeck’s album “Time Out” (ha ha) features songs in unconventional time signatures, like his really famous piece, “Take Five”, in 5/4, and the aforementioned “Blue Rondo a la Turk” in 9/8 (which can be counted as though it were in a really fast 3/4, but is pretty clearly in 9).
Nine Inch Nails have a song called “March of the Pigs” that could be in alternating measures of 14/16 and 15/16, or in three measures of 7/8 and one of 8/8, or even in 7/8 with an extra measure of 1/8 every four measures. What it boils down to is when you’re listening to it, you count:
“one-two-three-four-five-six-se’n
one-two-three-four-five-six-se’n
one-two-three-four-five-six-se’n
one-two-three-four-five-six-SE’N-EIGHT,”
and you’re back at the same place in the melody’s loop.
The same album also has a song in thirteen, or possibly in alternating measures of six and seven, with an acoustic guitar bridge in 3/4. It’s amazing.
Hope I’ve cleared it up.
On preview, I see that Eonwe has explained this much more concisely, but dammit, I typed this all and I’m not letting it go to waste.