Thanks for writing. The best time to prune the type of hydrangea you have is right after it finishes blooming.
To encourage more blooms, be sure it's growing in moist, well-drained soil that's rich in organic matter. Topdressing the soil with an inch or two of compost every year helps a lot, as does spreading a layer of mulch over the soil around the plant.
Hydrangeas can be heavy feeders, so if your soil isn't particularly rich, fertilizing the plants (with a general-purpose garden fertilizer) in early summer can be helpful.
---Justin, Senior Garden Editor, BHG.com