The following tips all stem from the general principle of economizing one's motions. For a more complete answer, look up an article of mine that was published in the October 1994 issue of The Strad, called "Cello Technique Made Simple." The more extraneous motions you use, the harder it is to play fast. The weakest link in the cello playing chain when playing fast is wasted motions, since they waste time and energy. I will divide my response into two parts, the right hand and the left hand.
1. The Right Hand
The bow is usually the culprit when one has trouble playing fast. Naturally, there are left hand problems too as you will read later, but many perceived left hand problems can be traced to troubles with the bow instead.
a. Always know what string you are on
The faster you play, the harder it is to keep track of which string you are supposed to be playing on. Work on the transitions between strings. Try playing the passage on open strings with your left hand fingers "ghost fingering" above the strings.
b. Always know which direction you are bowing
The faster you play, the harder it is to keep track of which direction your bow is supposed to be going.
c. Keep your right elbow in an elevated position as if playing on the upper string
If you have a lot of string changes, keep your bow arm elevated to the level of the upper string. Your string changing motion will then be done more with wrist and lower arm movement. Don't let your arm flap up and down with string changes like a wing.
d. The faster the notes, the less bow you need If you are playing fast notes on separate bows, use very little bow. You may find that you can use as little as an inch (2.54 cm for you Europeans) or less.
2. The Left Hand
a. Use Good fingerings
This is a VERY lengthy topic by itself, good fingerings vary depending on the needs of the particular passage, both technically and musically, and there are so many exceptions.
But anyway, here are a couple of ideas. Look for scale fragments in the music so that you can use tried and true quality scale fingerings. Shift after longer notes and group the fast notes together under your hand if possible. Find fingers that take advantage of rhythms. For instance, when you have two sixteenth notes followed by an eighth note, finger it 1-2-4 (under the hand) instead of 1-2-1, ie. don't shift in the middle of this figure.
b. Minimize finger motions
You don't ever need to lift your fingers very high when you play , but it is especially critical when playing fast. The higher you raise your finger, the longer it takes to return to the fingerboard when it needs to be used. Depending on where you're playing on the cello, you can get away with lifting your finger as little as 1/4" or so (7mm).
3. Don't type on the cello
A common problem is that people will lift their non-playing fingers as they play. This really slows down the hand. You simply don't have time in the fast passages to lift a finger and put another down. Keep the unplaying fingers down on the fingerboard. Then, when you lift a higher finger (ie. the 4th finger), the lower finger (ie. the 3rd finger) is already in position.
Tim Janof