The first thing you'll need is a good uke. If you live in the Richmond, VA area, there really is no better place to get a uke than Fan Guitar and Ukulele. Just give them your budget and they will show you the best options. Be sure to get a case for your uke and a good clip-on tuner. I recommend this one. This is a great music shop to just hang out and marvel at all of the ukes they have there. they offer private lessons, as well!
Print out this ukulele chord chart:
Now, commit to learning just three chords, in this order: C, F, and G.
Strum gently using your thumb or index finger, and work on switching naturally and smoothly between these chords. You can play them in any order you want!
When you are ready, take a look at the chart for the song "Three Little Birds," by Bob Marley. If you can play C, F, and G, and can move fairly smoothly between them, then you can play this song! Just strum using downward strokes on the steady beat, and give it a shot. Take a look through the song list here for some more tunes to play (some really easy 3-chord songs are "I'm a Believer" and "Lean on Me."
Gradually increase the number of chords you can play, using the simple chord chart above. If you know all of the chords on the chart and can move smoothly between them, there will be no stopping you!