Of all the instruments, our students seem to have the most trouble changing strings on mandolins. Somehow, banjos and guitars aren't as much trouble to change strings on as a mandolin is. So here are a few tips to make it easier changing mandolin strings:
1. Don't take all the strings off at once! Change just one at a time. This will help keep the bridge in the right place.
2. Wind each old string down, one at a time, and unhook it from the tailpiece and tuner posts. When you're removing the old string, some tailpieces (and some tuning machines) can be VERY difficult to deal with, especially if the strings are so old they’ve gotten rusty. If you have a pair of wirecutters handy, and a pair of long-nose pliers, those two tools can make it a lot easier to get (or cut) the old strings off.
3. When you're putting the new strings through the tuner post-holes, be sure to leave enough to make at least 2 1/2 or 3 turns around the post. This helps make sure the string won't slip around the tuner. Conversely, DON'T wind the whole string-length, right out of the envelope, around the post-- it might take up ten or fifteen turns or more, and it'll be a real mess tightening the string up as well as making it harder to get the string off next time you change them. 2-1/2 or 3 turns are fine.
4. When the string's up near proper tension, carefully cut off the extra length. DON'T poke any part of yourself (fingers or eyes, especially) with the end of the string!
5. As you change each string, tune it to its pair-string (E to the other E, A to the other A, etc.) and then bring it up to pitch with an electronic tuner. And when you’ve changed each string, re-tune all the others, because they'll all be stretching. It's not necessary at this step to have them EXACTLY in tune, but get them pretty close.
6. When all the strings are changed, re-tune them all with the electronic tuner. Then play a tune or two and re-tune the strings again. Do that two or three times. (This is not a grind. Remember, it's fun to play!)
7. Re-tune the mandolin before putting it away, and then re-tune it the next day. At that point the strings will usually be stretched out, and you'll only need to do "regular" tuning from then on.
If your mandolin's tuner-buttons are hard to turn, you can try putting a small drop of oil on each tuner's gears from the back. If you do this as you change strings, you can apply the oil with the string off and turn the tuner-button a lot of times to work in the oil. This usually helps the tuner turn more smoothly.
Good luck with the strings!