When is the best time for pruning/triming? Will the tree not produce fruit the following year where trimmed?

All depends on what variety you are dealing with. Normally trees are pruned after harvesting their fruit. If it is an early variety, you would prune right after picking is finished and the tree would recover well during the rest of the growing season. If it is a late variety like Monroe, when picking is finished in January the tree does not have much time to recover to fruit next season.
Also, all depends if if it light pruning or heavy pruning. 
Some people will do the top of the tree one year, the east and west sides another year etc. I really don't prune much.