The closure of the service will happen in three stages, beginning on 1st April. From this date onwards there will no longer be any product registration cards bundled with games, meaning products cannot be registered with Club Nintendo.
20th April will drop the ability to register digital products bought from Nintendo's eShop, meaning those products will no longer appear in the 'My Registered Games & Systems' section of Club Nintendo.
And finally, on 30th September Club Nintendo will fully shut down, meaning no more registration, earning Stars or exchanging Stars for items. Make sure you spend your Stars before this date, as they will expire.
Nintendo say they are making a new programme to replace Club Nintendo, launching later this year, but no further details have been revealed yet. However, users that sign up to the new programme during the launch period (whenever that will be) will be able to download Flipnote Studio 3D for 3DS completely free.