To put it (fairly) simply, the top number is how many beats per measure, the bottom number is what kind of note is getting a full beat.

So in 4/4 time, there are four beats in a measure (that is to say, you would count to four before moving to the next measure) and the quarter note receives a full beat. Since a beat consists of a number and the "and" following it ('1 + 2 + 3 + 4 +' in 4/4 time), you would count each quarter note as "1 +" (or "2 +" or "+ 3" and so on).

An eighth note is half of a quarter note, so you have to give it only half the count. Count it as just the "1" or the "and." A sixteenth is half of an eighth, so you have to give it half the count. For sixteenth notes, we break down "1 + 2 + 3 + 4 +" even further into "1 e + a 2 e + a 3 e + a 4 e + a." So a sixteenth note would be counted as "1," "e," "and," or "a."

Half notes have twice the count of quarter notes, so you'd count them as "1 + 2 +." Whole notes have four times the count of quarter notes, so they'd be "1 + 2 + 3 + 4 +" (the full measure).

And then you have dotted notes. A dotted note increases the value of a note by one half. So a dotted half note would be counted as "1 + 2 + 3 +" and a dotted quarter note would be "1 + 2" and so on.

So let's say you have a four-bar riff in 4/4 time. We'll let "Q" be a quarter note, "E" be an eighth, an "S" be a sixteenth, "H" be a half, and "W" be a whole. A period after any letter will indicate a dotted note of that type. The italics underneath show the count. You play on the notes that aren't in parentheses, and hold the note as you count the numbers within them.

|-H-----------E----E---S---S---S---S---|-S---S---E---E.---S---Q-----Q----|

..1(e+a2e+a)..3(e).+(a).4.....e....+....a........1....e....+(a)2(e+)a....3(e+a)4(e+a)

|-H-----------E----E---S---S---S---S---|-W--------------------|

..1(e+a2e+a)..3(e).+(a).4.....e....+....a........1(e+a+2e+a3e+a4e+a)



I hope that helps at least a little bit.