I'm gradually getting the hang of it. First, as has been mentioned previously, you really do need to the the chord changes so that they're automatic. It's kind of like doing math problems... once you see how to do one of them, all the others (of that type, at least) are suddenly do-able. The other thing I usually do is hum the song as I play it before I try to sing words. It's easier (for me) to get the melody and the strumming down before I start worrying about getting the words right.
If you think it's hard to play uke and sing, you should try playing BASS and singing! Single notes which aren't necessarily what you're singing, and might not even have the same rhythm! Whew! I don't know how people like Paul McCartney and Geddy Lee do it! I'm getting better at that, too. So far though, I just sing some backup when I play bass.