The first time you find a cursed coin, it automatically goes into your inventory. You can't get rid of it. Whether you put it in a treasure chest or give it to one of your officers, it jumps back into your inventory.
At night you turn into a skeleton. You can not change your appearance back to your normal choice of appearance. You will be attacked by anyone you meet.
After a while, your ship's sails will appear torn, and the ship will emit a cloud. These have no effects except that if you are in 1st person mode on deck, the fog impedes your vision. It does not have the effect of a smoke screen hiding you from the enemy!
Each cursed coin reduces your Luck by 1. Unlike other items which give bonuses or penalties to your skills, this is cumulative.
While you are a skeleton, you have increased hit points.
If you get additional coins, you can give them to your officers or put them into your ship's locker, where your crew will pick them up. Your officers or crew then also become tougher. Crew who have been cursed do not need food or rum, being skeletons. (This does mean that they do not gain morale from food or rum consumption, so it may be harder to keep morale from dropping.)
How did Jack Sparrow get rid of his curse?
First you must travel to Tortuga, alias La Tortue, and visit the tavern. There you will meet Joshamee Gibbs, who will give you a compass. (He will also volunteer to join you.) If you now look at the worldmap, you will see a small island, Isla de la Muerte, which was not there before. Sail there. Isla de la Muerte has two landing spots. One has a wrecked ship which is the home of Hendrick Vanderdecken; this is not the place where you will dispose of the coin, though it is worth visiting for other reasons. The other landing spot leads to a cave with a treasure chest in which are 881 cursed coins. Putting yours in there brings the total to 882 coins and lifts the curse. From now on, any more such coins which you find are not cursed and can be sold.
If you've read the "Good stuff", you may want to keep the curse active and even take more coins from the chest to spread the effects among your officers and crew.