That or which

"That" should be used with restrictive clauses and "which" should be used with non-restrictive clauses. A non-restrictive clause will always read as an aside - e.g. - The dog, which had brown fur, was eating its food. In other words, the sentence would still make sense if you removed the clause altogether. (The dog was eating its food)

A restrictive clause, or defining clause, is essential to the meaning of the sentence. E.g. - The dog that had no teeth could not each its dinner. If you attempt to remove this clause, you will lose the key piece of information in the sentence.

As you will also note from the above examples, non-restrictive clauses need a comma (before the "which"), while restrictive clauses should not have a comma (before the "that").  

That or which should only be used as a pronoun before an inanimate object or an animal. If referring to a person, it should be who.