Ukulele strings don't have many of the problems that guitar strings have. They won't corrode and start to sound dull, and they will last for several months. Change your strings if they start to look nicked and damaged from being picked aggressively or banged against the frets, or if they start to lose their tuning easily. Change them all at once to prevent the old strings from going bad unexpectedly.
Loosen the string you want to change until it is slack. Then, unwind it with your fingers and pull it out of the tuning lug.
Pull the string out of the bridge. There will be a knot holding it in a slot behind the saddle. Push the string through the slot and discard it.
Tie a knot at the end of your new string. Thread it into the slot and over the bridge like the string you just replaced.
Thread the string into the hole in the tuning peg and tighten it. If you have a standard headstock like the one pictured below, tune the strings so that they are on the inside sides of the pegs as in the picture. If you have a slotted headstock, tune the strings so that they are on the tops of the pegs.
Stretch the string by pulling it in the middle as you tune it. Ukulele strings have to stretch quite a bit before they will keep their tuning. Stretching yours by hand will help it stay in tune more quickly.
Cut off the end of the string with a scissors or wire cutter.
Do not restring your ukulele immediately before a performance. It will not be able to hold a tuning well for the first few days.