The first pruning of the year should take place after the last frost of the spring.  Cut away all of the dead parts.  Follow up with a good watering and some fertilizer.  Be sure to carry away the clipped branches because sometimes diseases can breed in them. 

Some people try to start laurel shrubs by digging up wild species, but this is often illegal, and will probably not result in a very healthy plant.  The best quality of plants are those from a good nursery that have the roots balled up in burlap.  When you plant the laurel shrub, you will want to plant it somewhat shallow.  Follow the directions given to you by the nursery, though, because there are many different types of laurel. 

There is another laurel that is a totally different type of plant and that is the bay laurel.  This tree is very sensitive to cold, so must be kept in a container indoors during the winters in cool regions.  The leaves are the bay leaves used in seasoning soups and stews.  This plant is known by the Latin name, Laurus Nobilis, and was used long ago to make victor's crowns in ancient Greece and Rome.