Indirect Free Kicks
There are four offenses in Law 12 specifically aimed at the goalkeeper. An indirect free kick is awarded to the opposing team if the keeper, in the penalty area, commits one of the following:
Takes more than six seconds, after controlling the ball with the hands, to release the ball into play.
Six seconds is not hard and fast; referees are instructed not to count or signal publicly, and first offenses are usually given verbal warnings. But six seconds is plenty of time to settle the ball, jog up to the edge of the penalty area and find an outlet. During this six seconds, the goalkeeper can move anywhere in their penalty area. Don't get caught by this Law - instead, use it as a reason to work on quick distribution to start the counterattack.
Touches the ball again with the hands after releasing it into play, before the ball has been touched by another player.
Bouncing or softly tossing and catching the ball are not considered "releasing the ball into play", but why even risk it? Bouncing the soccer ball is a holdover from olden days where a goalkeeper was able to move in the penalty area if they bounced the ball (similar to a basketball dribble). That rule no longer applies, so once the keeper has the ball safely in their hands, they should hang on to it until they are ready to deliver it downfield.
Touches the ball with the hands "after it has been deliberately kicked to him by a team-mate".
The italicized above is a direct quote from the FIFA Laws, and is often misunderstood. Remember the intent of the Law, which is to prevent time wasting by the defense. As such, only a deliberate kick by a teammate, either to the goalkeeper or to a place where the goalkeeper can safely pick the ball up, should be penalized. An accidental deflection off a defender's foot, or a missed clearance that falls to the goalkeeper should not be penalized.
But as always, "deliberate" is in the opinion of the referee. So if in doubt, don't pick the ball up - unless the ball is at risk of going into the net if you don't use your hands! In that case, better to concede an indirect free kick than a goal.
Touches the ball with the hands directly from a throw-in from a teammate.
The goalkeeper may still be used as a target for a throw-in, but they must handle the ball with their feet like any other player.
An indirect free kick can also be given to the goalkeeper's team if an opponent prevents the ball from being released into play by the keeper. This is seldom called, but it's good to know the keeper gets a little protection in the Laws!
Finally, it is an indirect kick if an opponent plays in a dangerous manner. This applies not only to endangering an opponent (e.g. high boot) but also to endangering one's self (this is why the player on the ground is called for this - they have put themselves in harm's way). By tradition, the goalkeeper is given leeway here and is allowed to put themselves in positions that would be dangerous for any other player on the field (for example, sliding at the feet of an attacker).