Your question only asks about nouns - "things" to name, but verbs, adjectives, whole other categories of words exist your child will need to know too.
Play games. Hide things and use directional words to direct your child to the hidden object. Then, let them hide something and help you "find it".
Play games like "down by the bay" where you have to come up with sets of words that rhyme to make it funny. There are tons of "games" you can play with words that encourage rhyme like this. Do this in the car or while waiting for an appointment. Do it often.
List all the words you can think of that start with a favorite sound. A great way to get this started, is teach your child the first sound in his/her name. Then say what else starts with that sound. Offer a few examples and then brainstorm together. Do this when standing in line at the grocery, at the bank, wherever. Point is, do it often.
Play Eye Spy and describe things to teach an adjective vocabulary.
Do sensory activities to use additional descriptors. What does the Gak feel like? is it slimy, smooth, rough. . .? (for some examples of sensory activities you can access some on pinchxeverything.blogspot.com or at almost any site for preschool teachers.
Do lots of sorting and classifying. Find a bunch of old buttons and "sort them" together. Let your child describe why each button goes in the pile he has chosen. Are you sorting by color, shape, or something else?
Encourage your child to tell you stories about the pictures he/she draws. Ask so do you mean? and then use synonyms for at least one or two words occasionally during the sharing of this story.
As some one else said, READ READ REAd and then READ some more. Read the same books over and over again. Your child doesn't have to actually do the reading - its pretty early to learn to read, but you can read together. Choose books with refrains and encourage your child to say the refrain with you.
Spend time together and use "big words" alongside synonyms you know he already understands. Avoid baby language. Talk and then listen (even if he makes little sense, listen and paraphrase what you do understand). The, listen and then talk some more.
Cook together. Let him do the mixing (and maybe even egg breaking), he can probably slice bananas with a butter knife when needed. Talk about what you are doing as you do it. Your child will learn all sorts of nouns and verbs from this activity.
Go on nature walks. Describe everything from how the weather is and how the air feels to the way the ants move along the trail. Go slow and move at his pace, stopping to look at things he wants to inspect more fully. Ask lots of questions about what he is experiencing, seeing, feeling. . .
Fill his world with poetry - nursery rhymes, great children's books and song.