If your ball is in or touching ground under repair, an animal hole, or temporary water such as a puddle, you get free relief, and you get it too when one of them gets in the way of your stance or swing. You drop a ball within one club-length of the nearest spot that gets you fully clear.
What counts?
Four kinds of things come under the same rule: animal holes, ground under repair, immovable obstructions and temporary water. Temporary water is water that has collected on the course and isn't in a penalty area, such as a puddle after rain. Free relief is not available from the same conditions when your ball is in a penalty area, or when the condition is out of bounds.
How do I take relief?
In the general area, find the nearest point of complete relief, then drop within one club-length of it, no nearer the hole, in the general area. You must be completely clear of the condition. The dropping steps are in Taking relief: measuring and dropping correctly.
On the putting green, place the ball on the nearest point of complete relief instead of dropping.
What about in a bunker?
You can take free relief inside the bunker. If there isn't a spot in the bunker that gets you clear, use the spot with the most relief available there. Or, for one penalty stroke, you can drop outside the bunker, on the line behind the ball.
What if I can't find my ball?
If it is known or virtually certain that the ball is in the condition, you can take the same relief using the point where it last crossed into it. If you only suspect it, the ball is lost (see A lost ball).
The governing rule is Rule 16.1.
Local rules
Your league's committee may have local rules that change this. Ask the organizer which ones your league uses.