Look for a relative pronoun -- who, whom, whose, that, which, where, when -- in your sentence. Such words typically introduce adjective clauses, and an adjective clause normally follows the word it modifies. For example, suppose you have the sentence "Athletes who perform in the Olympics must spend years in training." The phrase "who perform in the Olympics" is an adjective clause describing "athletes."
Recognize that sometimes the relative pronoun is dropped from the beginning of an adjective clause. For example, consider the sentence "The mug I use most often came from the 1984 Olympic Games." Here the relative pronoun "that" would normally occur after "mug," but in casual uses it may be dropped. The adjective clause would be "that I use most often."
Understand the concept of an essential clause, also called a restrictive clause. Some adjective clauses are needed to make the meaning of a sentence clear -- they are essential for the sentence to make sense. In this situation, the clause must not be set off with commas. For example, examine the sentence "Tourists who travel to the Olympic Games stay in hotels." This sentence refers to only a select group of tourists rather than tourists in general.
Examine if your sentence contains a nonessential or nonrestrictive clause. An adjective clause that adds information to a sentence but is not necessary to make the meaning of the sentence clear is nonessential. For example, consider "The Columbia Broadcasting System, which televised the 1998 Winter Olympics, set up a website for the athletes." Here you could remove the adjective phrase "which televised the 1998 Winter Olympics," and the sentence would retain its meaning.
Examine whether the adjective clause begins with "that" or "which." Typically, "that" will introduce an essential clause and "which" begins a nonessential clause.