Checkmate is the goal of the game, there are many ways to get there...
Typically
The first 10 moves (roughly) are typically called the opening phase.
In the opening, there are usually 3 goals.
1. Develop your pieces (they do very little in there starting squares). Consider a knight on it's starting sqare (c1 or f1 or d8/c8) vrs one in the center of the board, the same thing holds true for bishops and rooks which don't even have the advantage of being able to jump pawns.
2. Safeguard your king. Usually this means castling.
3. Control central squares (e4, e5,d4,d5 and potentially c4/5 and f4/5). This allows you to quickly move pieces into the critical areas - center kingside or queenside while your opponent may have a harder time of this.
The MiddleGame.
Outplay your opponent by starting an attack on hiis king, try to win material or gain some other sort of advantage (see #1 in the opening phase - make his pieces bad/blocked and yours good). The key here is to use all your pieces, not just your queen, as more force vrs. less for
The Endgame (checkmate in an earlier phase clearly precludes this) starts when there are only a couple of pieces left on the board.
At this point, the kings don't have to worry about being mated and become forces to be reconed with. The goal here is typically to queen a pawn and win due to the material advantage.
Hints:
If you are up material, trade down as your advantage becomes more noticable the fewer pieces there are around.
All rules can be broken if done properly.
Personally, I suggest that everyone learn these simple mates (K+R vrs. K, K + Q vrs. K, B + B +K vrs K) as you can then win most endgames where you are up material. Other than that, study the game if you care to or just play for fun.