It is a good idea for most folks to change strings one at a time. This will keep the bridge in place and retuning will not be as difficult. Maybe every 3rd or 4th time, take them all off and clean the fingerboard, etc. Try some 0000 steel wool up and down the fingerboard. This cleans the frets very well. A bit of lemon oil is good if you don’t play that often. If you play a lot, you may not need to add a thing. I’ve played my banjos a good bit over the last 25 years and have never put a drop of oil on it. Just clean it, string it, and go!
Attaching the strings to the tuners can be tricky. The string should wrap at least 3-4 times around the string post but not much more. Either too much or too little can cause strings to slip out of tune. The string should wrap in a tight coil down the post from the hole. After slipping the string through the hole, leave enough slack in the string to fit a softball. That should give you the right amount of string around the tuner.
Start tuning to pitch. Stretch the string a bit to help seat it at the points of contact (bridge, nut, and tailpiece). If you hear a creaking sound while tuning, the string might be binding at the nut or bridge. The slots at either one should be the same size or just a bit wider than the string. Some graphite in the slots is an old trick that can help the string slip through the slot easier.
First, poke the string through the hole and then tuck it under itself in the opposite direction you will be turning the tuning peg. Next, pull up on the end of the string and put a kink in it.
Use your index finger to hold the string tight and use your other fingers on that hand to pull the string towards the palm of your hand until the string gets tight enough.
More on Strings
How often strings should be changed is up to the player, depending on how often and how hard they play. One thing to keep in mind is, whether you play them or not, the strings are under tension ALL the time. After awhile, they stretch and wear out. If you play a lot, the strings will lose tone and volume. They die so gradually that you hardly notice it until you change them. Suddenly, after changing the strings, the tone of the banjo comes back to life and they will stay in tune better. Someone who plays every day may need to change their strings every two weeks or even sooner. Less frequent playing could require only changing the strings every two to three months. For the sake of staying in tune, change them fairly often. You may find that the 4th string seems to die much quicker than the others because the wound string traps more dirt and grime. I recommend changing the wound 4th string a little more often. The tone of the 4th string is critical; if it’s dull and mushy sounding, it can make the whole set sound bad.