the chords are:
a-0-2-2-5-3-
e-0-1-3-5-3-
c-0-2-2-6-4-
g-0-0-0-5-3-
GCE & A are the strings...so the order in this diagram is the order they would be in if your holding the uke as if your playing it, then tilted towards you so you could see the strings (if that make sense)
The numbers indicate what frets you need to put your fingers on. You read from left to right so strum all the strings, holding none of them down on the fret board (ie open) this is represented by the column of "0" in the diagram,
Next, you strum all the strings again, but this time you hold the C string and the A string down on the 2 fret, ans the E string down on the 1st fret. That is a G7 chord and looks like this:
The next column of numbers moving to the right represent a G chord, and looks like this:
Then, just keep moving your fingers to the locations shown on the diagram as you read from left to right...
hope that helps...
Edit: Bar the last 2 chords, in other words, lay your index finger across the 5th fret to cover all the strings, then use another finger(ring or middle) to press the C string to the 6th fret..