What type?

You normally do not have to do pruning (minor pruning is 'ok'; say to remove crossing stems, dead wood, a branch that is too long, etc).

Climbing hydrangea, Hydrangea macrophylla (mopheads and lacecaps), Oakleaf Hydrangeas and Hydrangea Serrata all produce invisible flower buds near the end of the stems in Julyish and they open in the Spring so, be careful pruning these (maybe wait until after they bloom but before July so you get to enjoy the bloomage). Remontant varieties of these hydrangeas will bloom on new wood too so you get some bloomage thru the year no matter what. If you were to prune these remontant ones, you would probably get some blooms during 2015.

Rule of thumb: if the shurb is planted where it can grow to its advertised width/height, you should not need to do major pruning at all. But take a peek now that most are just sticks (although mine are leafing out) and see if you need to do selective pruning of crossing stems, etc.

Deadheading of spent flowers that are stiiiilllll hanging around is ok but that is not the same as pruning, of course.