Notes for tuning the four strings of the violin:
A (the second highest pitched string, one from the left)
D (left of A, sounding a 5th lower)
G (the lowest sounding, thickest string all the way to the left)
E (the highest pitched, thinnest string all the way to the right)
This is the typical order for tuning the string of the violin. In an orchestra all instruments tune to the A, which is why I start with the A here. I also think it makes for a more in tune instrument to start with a middle string and tune outward.
I ask beginning students to tune with the tuning SCREWS, located next to the tailpiece and the bridge, and NOT the tuning PEGS (larger, located in the pegbox next to the scroll). Turning a tuning peg too far in the wrong direction can easily break a string (and they are pricey to replace). Tuning screws typically cannot make such large adjustments.
Tuning With Double Stops:
Tune the A string alone, than play the A and D together in a soft, smooth double stop and tune to a perfect fifth. Then play the D and G together and tune to a fifth. Last play the A and E together and tune to a fifth, typically using a tuning screw and not the peg for the E. I prefer an instrument tuned to perfect fifths rather than an instrument tuned to a tuner or a piano. Yes, it's different. String instruments are not designed for equal temperament (the way pianos are tuned) and will never ring to their full potential or play double stops completely in tune if they are not tuned in fifths.
Tuning Without a Reference:
If you can tune with double stops, tune the A by ear and then tune the instrument by fifths. If you can't tune with double stops: start with the G string, add fingers 1, 2, 3, 4 keeping them in tune as closely as you can. Tune the D string to the same pitch as the fourth finger (D) on the G string. Play 1, 2, 3, 4, on the D and tune the A to the same pitch as the four on the D. Repeat with A and E.
New strings go out of tune quickly as they adjust to the high degree of tension they are kept at. Typically I will put a new string on at the end of a practice session, tune it, wait a minute, and then tune it again a whole step above it's tuning note and put the instrument away for the night. Then the next day it will only need a few adjustments, but will mostly keep it's pitch. If you have to play on a new string or strings immediately, simply tune the string very slightly sharp and expect to repeat every minute or two for 10 minutes, continue to check after that periodically.
Tuning Screws Versus Tuning Pegs:
Normally when tuning screws are added to a violin the strings are shortened slightly. This has a small effect on the quality of the sound, as shorter strings and not pulled as tight and do not sound as loud or bright. This effect is very small and not significant for beginners or intermediate students. These students should never shy away from putting tuning screws on all four strings (or having them put on at a shop) if they are not already on the instrument. Most professional players who play a lot outdoors have tuning screws on all four strings of their violin to facilitate fast and more accurate tuning. If you tune with pegs and it causes you constant grief, it's worth adding peg dope or taking the instrument in to a shop to have the pegs adjusted if necessary. They should turn easily and stick easily.