Violins with gut strings are tuned with the pegs (except the E string which is steel no matter what the other strings are). Steel or synthetic core strings allow for the use of fine tuners on all four strings. Normally you can tune your instrument the fine tuners. The strings are more likely to be flat (too low) than sharp (too high). To raise the pitch of a string, turn its fine tuner clockwise – like you were screwing a lid on a jar. And of course, loosen the strings by turning counter-clockwise. If you are loosening (lowering the pitch) and feel that the fine tuner is no longer engaged, you may need to use the peg first.
Check the fine tuners from time to time. Look under the tailpiece to see if they are getting close to the wood of the instrument. They can become so low that they actually gouge the wood. Needless to say, this is not a good thing.
When the fine tuners are tightened as far as they will go, you will need to “back off” the fine tuners all the way – until they are just barely engaged. Then take up the slack at the pegs and fine tune as needed.
Use the pegs when the instrument is far out of tune or after you have loosened the fine tuners. NEVER TIGHTEN THE STRINGS WITHOUT LISTENING AS YOU TIGHTEN! (… or you may break a string.) First listen to the pitch you are aiming for, then pluck the string and tighten the peg, listening as the pitch rises. Remember, the pegs are tapered. You’ll need to gradually push the peg deeper into its hole as you turn. It should be snug enough that it will stay in place when you’re finished.
If the pegs have become hard to turn, you can use a small amount of “peg dope” on them (available at any violin shop). If the pegs slip, use a bit of chalk. In order to use either peg dope or chalk, you’ll need to loosen the pegs (one at a time!) and pull them part way out of their holes. Some old-timers recommend using rosin on slippery pegs. I don’t recommend this as it may cause long lasting peg problems. Chalk works fine.
Occasionally, even on the best of instruments, the pegs and/or the holes they fit in may need to be re-done. Any professional violin shop can do this for you.