Probably the only piece on the board that appears weaker than a pawn is a king. The reason that the king appears weakest is that he cannot place himself in check. Placing a king in check is against the rules of chess. Because of this rule a king is typically very limited on the movements that he can make. Combine that with the fact that a king can only move one space per move and you have what appears to be a very weak offensive piece.
Using a king as an offensive piece should only take place during the end game in most situations. The end game is the point in a chess game where neither you nor your opponent has very many pieces left. Often times an end game is recognized by you and your opponent having one or two pawns and perhaps one primary piece each. At this point the offensive capabilities of your king become crucial in you having a chance to advance your pawn to your opponents back rank and getting a checkmate.
One of the best ways to use a king in this situation is to remember that two kings cannot be in spaces directly next to each other on the board because that is against the rules of chess. If you are able to keep your king in a favorable position that forces your opponent away from your pawns or primary pieces then you have a great advantage in the end game and will most likely win. While this is not the most complicated strategy, remembering that you can use your king as a buffer to limit your opponent's king during the end game is vital. Use your king in the end game to help assure you the win.