Problem Solving for the Cello
Fingers collapse, are weak, or don't move fast:
Practice finger exercises first very slowly, then gradually work for a faster tempo. Double stop exercises with an open string as the top note (found in Finger Exercises, Book One) are best for training the fingers to curve and play on their tips. Double stop exercises with a finger on each string (found in Finger Exercises, Book Two) are best for training strength and coordination.
You want better tone:
1. Strengthening the left hand is the first step. The fingers of the left hand must press the string down completely before the string can vibrate and make good sound. Try Daily Exercises for the Cello, Book One to help strengthen your hand, along with the Finger Exercises books (see above).
2. Bow training, first on open strings (String Crossing for the Cello, Book One), and then with fingered notes (Bowing Variations for the Cello, Book One). First, make sure your hand is relaxed while holding the bow. Feel the weight of your arm sink into the bow; don't squeeze the bow to get sound. Work on straight bows (try playing next to or in front of a mirror), and then work on making the strings vibrate as wide as possible with the bow.
You want to learn to shift:
Start with a book like Second Position for the Cello, Book One, or Fourth Position for the Cello, Book One. While shifting is best learned with a teacher, these books can offer considerable practice material for during the week.
When you first start shifting, you may hear some slides. It is much better to keep your finger on the string while you shift than to take it off, even if you initially hear more sliding; it is much easier to learn the distance between the notes this way.