Really only two ways to strum... up and down.
up-up-down-up, down-up-down-up, down down up down... just play with it, you'll get a feel for it. Us a pick, or just the backs of your fingernails... interesting sound when you use all four fingers. Check youtube for some examples of different styles.
On the uke, you can also pluck all four strings at once for a harp-like effect, or make a moving part by plucking the lowest string on the down beat and the other three for the balance.
You can also (with practice!) learn to pluck one string louder than the others, very cool effect to be able to pluck all 4 together and still bring out a particular note for a moving line.
Ukes are fun, have fun with it!