By far the most popular form of word play is the pun. Linguists who prefer big words call his paronomasia. What it boils down to is a word, phrase, or idiomatic expression with more than one meaning, or two words with the same sound but different meanings. The humor comes when you expect a word to mean something but it turns out unexpectedly to mean something else.
Rennick, Robert M.
Word Ways: Vol. 37
, Article 24.
Available at: http://digitalcommons.butler.edu/wordways/vol37/iss2/24