It's time for a new set of strings. How do I change all the strings on my violin (or viola)? What are the gotchas I have to look out for?
Ball end vs loop
Traditionally these instruments have a fine tuner on the highest string (E for violin, A for viola) which may take a loop end string. The lower 3 strings always take ball end strings. Modern violins for beginners and intermediate players will have a modern fine tuner fitted for all 4 strings which normally take ball end strings. Nevertheless it is worth checking your E (A for viola) string fine tuner to see if it is ball end or loop and buy your replacement string accordingly.
Removing the strings
The soundpost is held in place, not by glue, but by a combination of friction and pressure exerted by the tension of the strings via the bridge to the top of the instrument. If you remove all the strings at once you may be lucky and have sufficient friction to keep the soundpost in place but it's not worth the risk. Avoid the pain of having the soundpost fall by removing and replacing one string at a time.
Remove a string by first loosening the peg and turning until the string is completely unwound from the peg. Pull the string out from the hole in the peg. Unhook the ball or loop from the tailpiece or fine tuner. If you have a fine tuner then loosen the fine tuner to the maximum extent.
Installing the new string
I always start with the lowest string (G on the violin) and work my way up to the highest, which is the most delicate, the most likely to break and the most finicky to fit. Under a good light, thread one end of the string through the hole in the peg until about half an inch is sticking out the other side and start winding the string on the peg maintaining some tension in the string so it doesn't loosen. Go in the direction of the side of the peg box. The idea is that when you have finished the tightened string will be flush with the edge of the peg box so that it doesn't interfere with the other strings. Before going too far fit the ball or loop end into the tailpiece / fine tuner. Finish tightening when the string is taut but not tight.
E String Special Case
On the violin the E string is much thinner than the other strings, is usually made of a strong metal like steel and is under much greater tension. This means that left to its own devices it will cut into the bridge with bad consequences. The E string should come with a tiny plastic sleeve about 1-2 mm long. Make sure this fits in the groove in the bridge. This will protect the bridge from the string. Try also to make sure the plastic does not stick out from the bridge towards the fingerboard as this will affect the sound produced by the string. Try and have the fingerboard end of the tube flush with the edge of the bridge.
Tune the highest string last. On the violin I start with the G string and work my up. With 4 fine tuners I aim to tune up to no more than half a note below the desired note on the pegs first. I do this for all 4 strings ending with the E. The tuning on the lower strings will have changed so I go back and retune again using the pegs up to half a note below. Finally I use the fine tuners (which were previously completely slackened off) to complete tuning.
Over the next few days I find that I will play for 15 minutes and the strings will be out of tune as the strings bed in and stretch slightly so I'm retuning very regularly. Initially this will be with the fine tuners but eventually they will reach their tightest limit and I will then slacken off the fine tuner completely, tune roughly with the peg up to about half a note flat (less if I can manage it) before using the fine tuner again.
Just adding a bit to Brian T's well-done answer.
I recommend a cleaning step after removing the old string and before installing the new one. Wipe the notches in the nut and the bridge to remove possible FOD ("foreign object damage"), then run a pencil or other source of graphite powder into the notch to act as a lubricant.
Whatever else you do , **never EVER ** remove more than one string at a time! You want to keep the overall tension as close to operational as possible, to avoid stress on the bridge or soundpost.
Some bridges (most cello bridges have this) are built with a small insert for the highest-pitch string, made of an extremely hard wood. If your bridge has this, you probably don't need to use the plastic sleeve.
And after all strings are installed, re-inspect the bridge to make sure it hasn't warped or twisted as the new strings were brought up to tension.
Personally, I prefer to insert each string into the peg just far enough to stay in the hole until a couple winds are added -- rather than having the string end stick out the other side. I follow Brian's pattern of wrapping outwards and then back to lock down the string; I just find the image of the string end "flapping" around in the pegbox annoying. I don't think this affects the sound in any way.