Talk to your 3-year-old using adult language. While it may feel unnatural, adult language will expand your child's vocabulary by introducing new words.
Ask your child questions. Asking your 3-year-old questions forces him to answer you, which will build his language skills and vocabulary. As your child speaks with more regularity, it's inevitable that his vocabulary will increase.
Play games with your child and talk throughout the game. For example, if you and your child are using a toy oven to create make-believe dishes, say, "I'm going to cook pancakes for the customers, what are you going to cook?" Your child may not know what the word "Customer" means, so that gives her the chance to ask you what that word means. Even if she doesn't ask what something means, she'll still absorb the new words.
Ask your 3-year-old what certain objects are throughout the day. For example, if your child is in the living room, point to the couch and say "What's that?" If he answers something different from couch, tell him that the object is a couch and explain what a couch is.
Read to your child. Books help to spark your child's creativity and vocabulary. Read slowly and make sure your child understands the book. If she appears confused, explain the concept in clear terms.