The Basics
The bow is held in the right hand with the thumb bent underneath the frog to support it and the other hands loosely gripping the wood. There are many different holds and it its important to find one that suits your hand size and strength. The violin is held with the left hand, with the chin on the chin rest supporting most of the weight, and the fingers loosely coiled around the neck of the violin. The thumb should be relaxed but firm. The left elbow should be curved under the violin. The violin should be roughly horizontal and the right arm held high. The main methods of playing the violin are bowed and pizzicato.
Bowed
The bow should be drawn swiftly and smoothly across the strings, about halfway between the fingerboard and the bridge. A down bow starts with the hand close to the strings pulling across the string from left to right, and is generally used on strong beats. An up bow goes the opposite way, right to left, and is used on weaker beats and upbeats. However with practice down bows and up bows should be fairly difficult to distinguish. Slurs in music indicate that all notes within a slur should be played in the same bow movement. To play loud notes, the bow is pressed down harder on the string using the index finger or the bow is drawn across the string faster. To play more quietly use less pressure or draw the bow across the string slower. In classical music bowed music is indicated by the Italian term arco.
Pizzicato
To play pizzicato (often abbreviated to pizz.) the right thumb should be placed under the fingerboard and the index finger used to pull the string quickly upwards and across. For faster passages, the bow can be held while playing pizzicato, still using the index finger but without the support of the thumb. In more complex and advanced pieces, a small cross above the stave indicates the fingers of the left hand plucking the strings.
Fingering and positions
As there are no physical aids such as frets for violinists as there are for guitarists, accurate tuning comes with immense practice. On a full size violin, the tones are roughly two centimeters apart, but this is difficult to judge when playing since you are seeing from a different perspective. To aid tuning, it is very helpful to have a piano or other keyboard instrument when practicing.
The fingers of the left hand are conventionally named first (index finger) to fourth (little finger). When playing notes other than open strings (G, A, D and E), these fingers must press down hard, so that the string is shortened convincingly for a higher pitch. The standard intervals taught to beginners is tone, tone, semitone, tone (ie. G-A-B-C-D, D-E-F#-G-A, A-B-C#-D-E, and E-F#-G#-A-B). Of course the notes in between can be played by rearranging the hand position.
This is known as first position, where the first finger plays up to a tone above the open string. The next position usually taught is third position, where the first finger plays the note a perfect fourth above the open string (so, for example, third position on the A string would start on the D). All positions from first up to anywhere around tenth can be thus played, and two octaves on one string are considered fairly standard.
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