The first thing to note is that we mean ‘someone else’ here (i.e., another player or opponent) rather than you, your caddie or your partner and that you, the player, have nothing to worry about if that 'someone else' picks up your marker on the putting green in terms of penalties, but must make sure that you proceed in the correct way to remedy the situation.
The procedures come in Rule 9.7, which talks specifically about a ball-marker being moved, but with some cross-referencing back to Rules 9.4 and 9.5 which relate to a golf ball being moved.
Assuming an opponent is not lifting your ball-marker to concede the hole or match in match play, then Rule 9.7 has it all covered off with Rule 9.7a explaining what you must do to proceed correctly and Rule 9.7b discussing whether or not any penalties apply. Rule 9.7a says this:
If it is known or virtually certain that a player’s ball-marker is lifted or moved in any way (including by natural forces) before the ball is replaced, the player must either:
* Replace the ball on its original spot (which if not known must be estimated) (see Rule 14.2), or
* Place a ball-marker to mark that original spot.
As for any potential penalty to another player, Rule 9.7b highlights that this would only apply in match play, not stroke play:
If the player, or their opponent in match play, lifts the player’s ball-marker or causes it to move (when the ball is lifted and not yet replaced), the player or opponent gets one penalty stroke.
There are some Exceptions here that cross-reference back to Rules 9.4b and 9.5b, but assuming that we are talking about a ball-marker on the putting green, as would be the case 99% of the time, some of these would be largely irrelevant (e.g., when searching for or identifying a ball). You can read those Exceptions in full here.
