Tunneler, I think you've got it. I can also see how the fraction idea was confusing. The idea is that you have a measure with x number of beats (2, 3, or 4 beats) and that also gives an underlying rhythm. So the first question we ask ourselves is "How many beats are there?" = top number. Then we ask "Which note value gets the beat?" = bottom number. All the note values are proportional to each other so that two eighth notes last as long as one quarter note; two quarter notes last as long as one half note etc. If you know the beats and what takes the beat, then everything else falls into place.
Eventually you'll want to tackle a different kind of time signature called "compound" because you run into those a lot. It's the same kind of idea of a measure with x number of beats (2, 3 or 4 beats) but this time triplets get involved and the bottom number has a different role. These time signatures appear as multiples of three: 6/8, 9/8, 12/8 (6, 9 and 12 are multiples of three). Here our "beat" is a group of three:
6/8 (2 groups of 3 = 2 beats)
9/8 (3 groups of 3 = 3 beats)
12/8 (4 groups of 3= 4 beats).
3 what? The bottom number tells you the "what". In 6/8 time, 3 eighth notes (the "8") make one beat, so 6 eighth notes make 2 beats. They work like triplets.
Most of the time, signatures that have 6, 9, or 12 on top are in compound time with this triplet feel. There are clues like seeing dotted rests (one dotted quarter rest, instead of a quarter and eighth rest).