Read to your pre-literate child to familiarize him with words. After developing a basic understanding of the sounds that words make, he will more easily understand the concept of rhyming.
Tell the child that rhyming words have the same sound at the end but different sounds at the beginning. For example, "finger" and "linger."
Point to a body part and say a word that rhymes with the body part. For example, point to your leg and say "keg." The child should then be able to figure out the rhyming word "leg."
Point to a body part and tell the child to say words that rhyme with the body part. For example, if you point to your ear, he might say "deer," "hear" or "rear."
Go through the alphabet, starting with "A." Give the child a word from each letter, and then wait for him to use that word to make rhymes. For example, your game could start with you saying "art." At the letter "D," he would then say "dart."
Introduce your child to nursery rhymes by showing him the pages while you read. Nursery rhymes are a handy tool to teach the child other concepts as well -- for instance, using "Hickory Dickory Dock" to introduce the idea of telling time.