Try saying the sentence without the phrase in question and see if any meaning is lost. If it is, then the phrase is restrictive, which means necessary. If the total meaning remains the same, the phrase is nonrestrictive, which means unnecessary.

Example: Everyone uses the computer in my office; nobody, however, turns it off.

In this sentence, the phrase ‘in my office’ is a restrictive phrase, since removing it removes the identity of the specific computer and changes the meaning of the sentence. Everyone uses the computer is NOT the same as everyone uses the computer in my office.

At the same time, the back half of this compound sentence contains a nonrestrictive phrase in the word ‘however.’ One clue is that non restrictive phrases are usually set off by commas both before and after, while restrictive phrases are not.

And this is probably more than you wanted to know.