The ukulele (or uke) is like a small guitar with only four strings. It is descended from the Portuguese braguinha although the Hawaiians made it their own, messing with the tuning and slightly altering the design. It is an exceptionally easy instrument to pick up, unusually cheap to buy and manufacture, and supremely portable - all of which goes a long way towards explaining its faddish explosion of popularity in the last few years or so, with many singer-songwriters taking it up and quite a lot of clubs and open mic nights dedicated to it. The Ukulele Orchestra of Great Britain also deserve some credit for that, as does Amanda Palmer, whose delightful Ukulele Anthem notes that it only takes about an hour to teach someone the ukulele - 'about the same to teach someone to build a standard pipe bomb (you do the math)'.
Obviously it takes more than an hour to learn how to play the ukulele well. That really is long enough to learn how to knock out one or two three-chord pop or rock classics of your choice, though. With only four strings to worry about, and many common chords only requiring one or two fingers on the fretboard, it is hard to imagine an instrument that is easier to get started on.
The tuning of the common soprano ukulele seems a little odd at first. Come to think of it, I've been playing for a few years now and it still seems odd: GCEA, with the G higher than the C but the other strings descending in pitch so that the A is the lowest string (but only one tone lower than the G). That high G (which makes this a 're-entrant' tuning) obscures the fact this is closely related to standard guitar tuning. This is easier to see if we think about the baritone uke first, a bigger and slightly deeper instrument with a gorgeous sound to it. These are generally tuned DGBE, which is exactly like a guitar missing its two lowest strings. That means that most guitar chords can be played on the baritone uke by just leaving off the E and A strings. Technically some of those chords will be inversions, but in my experience ukulele players seldom worry about such things.
A soprano uke is tuned to one fourth above a baritone uke, which is five frets' worth - apart from that pesky high G which is an extra octave higher. That means that chord shapes for the soprano ukulele correspond to baritone ukulele (or guitar) chords, shifted up by a fourth - so the shape of a D chord on the guitar becomes G on the soprano uke, G becomes C, and so on. That makes it pretty easy to transfer guitar learning to the ukulele, especially if you're comfortable with transposition.
What this means for someone wanting to tune a soprano uke is that it's probably easiest to start with the C string, since it's the lowest in tone, and work up from there: E should be tuned to the fourth fret of the C string, A to the fifth fret of the E string, and G to the third fret of the E string. If you've done it right, the G string will then be tuned to the same note as the seventh fret of the C string. If you're musically inclined, you can probably come up with a couple of other ways of tuning the thing.
One other thing about the tuning - some ukuleles go out of tune embarrassingly fast after you tune them, and some are physically incapable of being altogether in tune to begin with. This is not universal, though. Please try not to hold it against ukuleles in general.
Ukuleles are Not Guitars
The ukulele is almost never played with a pick - although I did once see a music shop selling fat uke picks made out of felt. Strumming a ukulele is fairly similar to strumming a guitar, but easier, and calls for a looser wrist, and strumming closer to where the neck meets the body. Because it's more delicate you can easily play the downstroke with any single finger, and it lends itself to playing the upstroke with a finger too. On the whole, fingerpicking is easier than the guitar - with only four strings, it's simple to assign your thumb and your three best fingers to a string each. You can also just use two fingers and a thumb, with the thumb taking two strings, which is probably easier if you don't have to alternate between those two strings - most people find that their index and middle finger are far more dexterous than their ring finger.
As I said earlier, most guitar chords can be played directly on the baritone uke or transposed for the soprano uke, but there are exceptions - these are where one or more note of a chord is played only on the low E or A strings. Guitar-A7 (soprano-D7) can't be played in the standard two-fingered way, for example, because that would leave out the A - you end up with a C#dim instead, although to be honest you can probably get away with it. To play A7 properly you can play a normal A chord with an added finger on fret 3 of the top string. Baritone-C7 (soprano-F7) requires exactly the same added note. On the bright side, some chords are much easier on the uke - guitar-Gm is always a pain, and doesn't transfer directly to the ukulele, but baritone-uke-Gm (soprano-Cm) just requires fingers on the third frets of the highest three strings. Baritone-Bm (soprano-Em) is a bit easier than guitar-Bm, too.
Transferring tabs from guitar to ukulele can be a bit involved, especially on a soprano uke where you have to deal not only with losing two strings but also that high G. Most tunes can probably be played in principle, but they might need to be an octave or two higher if you want them in the original key. To see some virtuoso fingerpicking that makes it clear the ukulele can be a serious musical instrument, check out Hawaiian uke legend Jake Shimabukuro.
Some local uke nights