Okay, first up, if this is too simplified...well, you asked for it...
First, typically when you see somebody describe a chord they will describe it as the fret positions from the top string (i.e. furthest from the floor) to the bottom string (you can probably figure out what I almost wrote here
) going left to right.
Okay, I told you that to tell you this. Start by learning the first three chords in the key of C - that would be C, F, and G. They are.
C = 0 0 0 3
F = 2 0 1 0
G = 0 2 3 2 (a lot of songs will use the G7 or "dominant 7") which is 0 2 1 2
Those three chords are the "I, IV, and V" chords respectively and will get you through a lot of songs! Probably 80% of popular music can be "faked" in the key of C just using those three chords!
Next, add the Am ("vi") and Dm ("ii") chord.
Am = 2 0 0 0
Dm = 2 2 1 0
You can now "fake" somewhere near 95% of popular songs (in or transposed to the key of C, of course).
And therein lies the beauty of the ukulele! This is especially sweet if the key of C happens to fit your voice well because you can transpose songs to that key and play and sing almost anything.
From there, the sky is the limit. The uke is obviously not limited to the key of C - that's just the easiest key for a newbie to learn - much the way G tends to be the easiest key to learn on guitar.
But, you can have a lot of fun with just the info presented above. Learn those chords, then seek out the two- and three-chord song lists and you can have fun for literally years before having to learn anything else - though I'm betting you'll get hooked sooner or later and be discussing theory in a year or two.
John