Firstly let me say that pilots who do not have any fear are downright dangerous!
Use fear as a tool for taking action. Learn everything that you can and practice drills, checks again and again. Do lots of "dry swims" on the ground - imagine you are in the aircraft and picture yourself performing exactly as you would like to!
Remember also that F.E.A.R stands for "False Evidence Appearing Real".
When we become anxious our breathing rate changes. However you can make a conscious effort to breathe in a relaxed manner and this will alter how you feel.
I also believe that fear can be somewhat infectious. If your instructor is afraid or shows signs of underconfidence then this will affect you also!