For a cello player, basic left hand technique is the basic foundation of all playing. Correct left hand technique will facilitate intonation, and will allow you to play notes over the whole range of the cello.
The purpose of the fingers of the left hand is to hold down the string, changing the note you are playing by changing the length of the string that can vibrate. Therefore, when you press your finger down to play a note, make sure you are pressing the string down enough to prevent vibration. However, you do not need to press too hard; only enough to hold the string against the surface of the fingerboard.
When holding down a note, you should also try to keep as little of the finger in contact with the string as possible. This will create a sharper, less muddy tone. One way to accomplish this goal is to curve the fingers, and playing on the ends of finger instead of the pads, where there is less flesh between the surface and the bone.