What are the various rules for placement of goal kicks?

These are all completely different situations.

• A goal kick can only be taken within the goal area (the 6 yard box). (Law 16)
• A drop kick means the ball is still in play. The goalie could as well throw the ball to a team mate.
• Free kicks can be awarded almost anywhere on the pitch. They're taken from where the previous offence occurred. (Law 13)