The plant in the photo appears to be a kind of weeping hemlock.  There are several varieties and their shapes and appearance differ somewhat so it's difficult to say what your hemlock "should" look like.  However, here is an example of a healthy specimen:

http://24.media.tumblr.com/8ecf84d2135be35dcdcdc8cfc47caf63/tumblr_mih8j6aMbK1qh9jr9o1_500.jpg

Conifers  are subject to winter damage, and severe drought and colder than normal winter temperatures have combined to injure many this year including hemlock.  Removing the dead parts and shaping the living branches is about all that can be done for the moment.  If growing conditions become more favorable, the plant's health will improve and it will be possible to achieve symmetry with judicious pruning.  However, it may take two or three years to achieve the desired effect.

Watering evergreens well until the ground freezes helps reduce winter damage.