Actually, I think it's an excellent question, especially for a beginners' thread.
I almost always start with Uncle Rod's Boot Camp, which as a couple people have mentioned is a great warm-up. I don't necessarily do the whole program but I do at least a couple keys. Any exercises (Uncle Rod's are my favorites) I like to get over with right away. I can't help but think that sounds like the wrong attitude, but I didn't buy a ukulele to exercise all the time. (Uncle Rod makes it fun, though, because having seen him here on UU it feels like having a teacher you really like.)
Another thing I do is extremely boring but I'm finding it extremely effective, and that's working a brief series of chord changes, over and over (and over... and over...), for as long as I can stand it or for as much times as I have, even if it's only three minutes. This works really well when there are a couple of chord changes in a song that I want to learn. I try to keep this to no more than one line of a song, and I repeat it over and over, sometimes watching TV, not necessarily making any sound. If it gets too boring but the chord changes are still not as smooth as I would like, I experiment with strumming patterns. I've found that even if I am working a chord transition for one particular song, the likelihood is good that that transition will come up again. Anyway, this is working well for me.
Finally, of course, I just play stuff. I try to be very careful to not play songs up to speed until the chord changes are smooth, and sometimes I am successful, because I don't want to practice anything "wrong" (meaning, I don't want to master anything that I'm not executing well). But sometimes I just get excited and forge ahead. And sometimes I noodle while I'm watching TV or something.
I agree with Lori that it's good to mix things up a bit. My chord-change thing I do for very short periods, partly because it's boring and partly because you can't rush muscle memory, but if I did nothing but that I would go berserk. When I sit down to actually play songs, I could go on for hours and not notice the time passing. It's not the ukulele if you're not having fun!
Thanks again for the great question. There are some really good tips here.