When changing the strings, it is important to change the strings one at a time to avoid moving your bridge.
Make sure that each string is wound around the tuner at least 3 times and tune it up.
Once all your strings have been replaced and tuned, give the wound strings a stretch to make sure they have 'settled' and re-tune the banjo.
How long your strings last will depend on a number of factors, including the amount of playing, sweat and soap residue. If you want to get longer out of your strings, wipe them down with a dry cloth after playing.