This is Vanhoutte's Spiraea (Spiraea x vanhouttei )in the Rose Family (Rosaceae). This shrub is a primary hybrid of two Chinese species: S. cantoniensis X S. trilobata. It is one of several Spiraea that go by the common name of Bridal Wreath Spiraea.
How you should prune it depends on what you want it to look like.
If you want to keep it tall, I would recommend taking out some of the lower branches to improve the shrub's outline and let more light into the center of the shrub. Start by rmoving dead wood and crossing branches.
If you want start over with a shorter shrub, wait until the end of winter and then cut the entire plant down to the desired height. It might be best to go down to less than a foot tall for a complete rejuvenation. In any case, still remove dead wood and crossing branches.