When holding the neck of your violin, ensure your wrist is curved and your posture is perfect in order to create a rich tone.
Make sure your left wrist does not "collapse". You should support your violin with your neck and shoulder. Your left hand must be free to move.
Keep your fingernails trimmed short. You should depress the strings with the tips of your fingers on your left hand, and you can't do that with long nails.
Your bow should move perpendicular to the strings. Lead your bow with your right wrist. The stick of the bow should be slightly tilted toward the fingerboard (away from your face).
Your bow should move between the fingerboard and the bridge. When closer to the bridge, it will be louder. Play closer to the fingerboard to play more quietly. (for the beginner: the fingerboard is the long, black piece running down the center of the instrument)
When playing quiet sections of music, keep using all the bow but press down lighter.
Practice! Practice! Practice! (As a guide, college majors are recommended to practice roughly 2 to 4 hours per day. At least an hour a day should be expected as a bare minimum for serious practitioners.)
A few more things:
The violin is tuned ( from low to high ) G D A E.
There are several positions for your left hand depending how close to your face on the fingerboard your hand is. The 1st position is when your 1st finger on the A string plays B, the 2nd position is when it plays C, 3rd when it plays D. When a change of position is required a number is printed above or below the score to indicate which finger is used to play that particular note.
Before playing the bow should be rubbed with rosin. You can buy some at any musical instrument store. Keep rosin in your left hand and rub the bow against it in the same way you play. Do not over do this, since it will result in the violin sounding harsh.
Bowing:
The faster you move the bow, the more rich the sound coming from the string will be. But make sure you get all the notes in before running out of space.
As you get better, pay more attention to how you move the bow. Changing directions (up to down, etc) is pretty much equivalent to taking a breath while singing.
Sheet music will generally include bowing notations intermittently. Feel free to pencil in your own, but make sure you don't contradict the printed ones. The "up bow" mark looks like a V and the "down bow mark" like a square missing its bottom side. Up means start at the tip, down means start at the frog which is where your right hand is.
