On the putting green you can mark your ball, lift and clean it, replace it, repair damage, and putt with the flagstick in or out. Mark the spot before you lift, or it is a one-stroke penalty.
How do I mark and lift my ball?
Put a ball marker right behind or right next to the ball, or hold a club on the ground there, then lift it. After you replace the ball on its spot, remove the marker before you putt. Lifting without marking the spot, or putting with the marker still down, costs one penalty stroke.
What if my ball or marker gets knocked on the green?
If you, your opponent or another player moves your ball or marker by accident on the green, there is no penalty. Put the ball back on its original spot, or put a marker there. If it is moved by wind or water after you've already lifted and replaced it, put it back on the spot it moved from. If it hasn't been lifted and replaced, play it from its new spot.
What can I repair?
You can remove sand and loose soil. You can fix damage such as ball marks, shoe damage, old hole plugs and animal tracks, using your hand, foot, a normal repair tool, a tee or a club, without slowing play. Aeration holes and natural bare or uneven patches aren't damage you can fix. If you go beyond restoring the green, such as making a path to the hole, the penalty is two strokes.
What about the flagstick?
You choose before you putt: leave it in or have it taken out. There is normally no penalty if your moving ball hits it. Don't deliberately move it off-center in the hole to gain an advantage. If you do and the ball hits it, the penalty is two strokes.
Can I test the green?
Not during a round. Rubbing the surface or rolling a ball to check the green is a two-stroke penalty. Between two holes you can roll a ball on the green you just finished or on a practice green.
The governing rule is Rule 13.
Local rules
Your league's committee may have local rules that change this. Ask the organizer which ones your league uses.