I'm sure there are others here that know more about this than I do, but I have been doing some tabs lately so here's a couple tips.
You might want to download some software like Power Tab. It is free and it will make the process alot easier. If you don't know any music theory or how to read music, just learning how to use powertab will teach you alot about written music and some theory. Of course the whole process is much easier if you know at least a little bit about theory, scales, reading music, etc.
When I start a song, the first thing I do is figure out what key it's in. Once you know that, you have the framework of chords and notes that you will need. It might help to jot down a list for yourself of the scale notes and the common chords in that key, so you can refer to it. If you can't figure out what the key is, try searching on google to find the original key of the song and see if that is it. Sometimes it is, other times not.
Also, right off the bat, you'll need to figure out what tuning the uke is in in the song that you are trying to tab out. Is it high g, low g, dgbe? This is of course essetial to figuring out what is being played.
I've only tabbed out songs that I can watch on youtube. And I would recommend starting with one that has a pretty good video of someone playing it. Make sure you watch the video in the highest resolution possible. And then it's just watching the hands and the strings and getting it down. It helps to have your uke handy when you're watching so you can attempt to form the chords and notes and see if the sound matches.
Most songs can be broken down into a number of sections that may or may not be repeated. So many times tabbing out a song isn't as hard as you might think because once you get all the sections figured out, you can do some cutting and pasting to build the song. So it also helps alot if you understand how to use codas and repeats.
Don't forget to use all the resources on the internet. There is a guitar tab out there for almost everything, and many times you can get the basic chords from that to get you started.
Good Luck!