I have suddenly found myself attending ukelele jam sessions and having quite a knees-up! I have also found that there may be quite a demand for an article about making chords specifically for a ukelele, and that is what this is.
The ukeleles I have seen are miniature guitars, working on the same principle but with certain differences. The first difference is that they only have four strings, and the second difference is that they are tuned in such a way that the chord shapes you make on them are the same as those used on the highest-pitched four strings of a guitar but in another key. They are tuned G C E A, and by drawing a diagram one can work out just about any 4-string chord on them. If you do not already know how to work out what notes are needed to make a chord, there are instructions on this site under the heading 'stuff about chords'.I am going to assume, though, that you already know what notes you need, and supply this diagram:
The idea of this is that you can see what note you get at any place where you press your finger on the fingerboard (yes, it's intended to look like a uke fingerboard). So you can print it out and if you have 4 shirtbuttons you can place them on the diagram at the places where you would have to put your fingers to get specific notes, and by this process decide what is and what is not a practical fingering for a chord.
I will try to illustrate. If we want the fingering for a C chord we need to know that a C chord has the notes C E and G in it, and then we can look at the diagram and discover that we already have those notes without putting a finger on, but we also have an A which we must change, and as you can see we can put a finger behind 3rd fret on the A string to make that into a C. The note doesn't have to be a C, but it must be one of the three in the chord. (incidentally, if we do not put a finger there, the 'open' strings give us a chord with two names: it is either C6 or it is A min 7 (see 'stuff about chords' if you do not know what these are).
But usually things are a little more complex. I am going to try to make a chord of B7. This chord has B D# F# and A (work it out if you don't believe me). I have never played this chord on a uke, so the first thing I will do is notice that we already have an A on the open A string. We can do this: E string 2nd fret, C string 3rd fret, and that leaves us in rather a difficult situation because we have no B yet and the B on the G string is quite a long way to reach if you are also leaving the A string open. So - We will change the open-string A to a B (2nd fret) and the G string will be made to play our A - a fairly easy fingering by which the index finger can go right across all strings and another finger can finger the D#. This leaves us in a position where we can turn the B7 into a plain B by putting a finger on the G String two frets above the barre (the barre is the finger that goes right across)
Work the others out for yourself - but bear in mind that we can move a fingering like that we have just made up and down the fingerboard without even taking our fingers off the strings, and although that will not be the only type of 7th chord it can be used if you are in a hurry and don't know another type. It was a B, but 1 fret down and it is a Bb.
The better you organise your fingerings the easier the instrument will be to play, so when playing a sequence of chords try to get the position of each as near as possible to the one you started with - unless you are looking for some special effect.