You can remove a loose impediment, such as a leaf or a stone, or a movable obstruction, such as a rake or a water bottle, without penalty. The one thing to watch is that if your ball moves while you do it, you can get a penalty unless you are on the putting green.
What is the difference?
A loose impediment is a loose natural object. A movable obstruction is an artificial object that you can move without much effort, such as a rake or a bottle. Neither counts as part of the challenge of the course, so you can remove it by hand, foot, club or with help from others.
What if my ball moves when I move one?
For a loose impediment, put the ball back on its original spot. Unless the ball was on the putting green or teeing area, you get one penalty stroke, except when you were searching for the ball, where there is no penalty. For a movable obstruction, there is no penalty. You replace the ball on the original spot.
Can I take relief if my ball is on or in a movable obstruction?
Yes. Lift the ball, remove the obstruction, and drop a ball within one club-length of the spot right under where the ball was, no nearer the hole. On the putting green, place the ball on that spot instead.
What are the exceptions?
Don't move tee markers when you are about to play from that tee. Don't remove something on purpose to change what your moving ball does. Once you have lifted or moved your ball off the putting green and have to replace it, don't deliberately remove a loose impediment that would likely have moved the ball if it had been taken away before. That is a one-stroke penalty.
In a bunker
You can remove both before you play. Touching the sand while doing it is fine. See A ball in a bunker.
The governing rule is Rule 15.
Local rules
Your league's committee may have local rules that change this. Ask the organizer which ones your league uses.