Participial clauses and phrases, which modify some part of the main or independent clause, must be separated by commas. The Senate adjourned today, having completed all its business. Singing in unison, the protesters circled the building and wouldn't let the workers enter the plant. Two independent clauses joined by a conjunction need a comma as a pause. Seven men were arrested this morning, and police vowed to find five more they say are involved in the operation.
Commas separate two modifiers of equal weight that describe a noun.
Meteorologists forecast another cold, dreary night in Pittsburgh. Parenthetical expressions, which are similar to theatrical asides, require commas because they are transitions and lead into the main clause. Some council members, you may recall, didn't want to appropriate the extra money for two new parks until residents demanded it. Dependent clauses require commas to be set off from the main clause. A good example of this is attribution.