When do I use commas with clauses?

A restrictive element is essential to the reader's understanding; a nonrestrictive element is not. Look at the following two sentences. In the first sentence, who arrived yesterday is a restrictive clause, that is, one that restricts, limits, or defines the subject of the sentence. In the second sentence, the same clause is nonrestrictive, that is, it doesn't restrict or narrow the meaning but instead adds information.
The women who arrived yesterday toured the island this afternoon.
The women, who arrived yesterday, toured the island this afternoon.

The use of commas in these two examples actually has a bearing on the precise meaning of the sentence. In the first sentence, who arrived yesterday defines exactly which women are the subject of the sentence, separating them from all other women. In the second sentence, however, the information who arrived yesterday is not necessary to the sentence. It does not separate the women from all other women. The clause adds information, but the information isn't essential to our knowing which women are being discussed.

It is you, as the writer, who must decide which kind of information to give and whether or not that information needs to be set off by commas.