I have only been riding for a year but I know that your upper body should always be very relaxed. While your riding you should think about relaxing your neck and arms. Should be a fairly light grip on the handle bars while climbing, unless there is a need to hang on.

Also, important to think about your pedaling motion. Think about pushing and pulling and/or pedaling circles. Somebody posted a link about pedaling technique, not sure which category it is under.

Kelly