Sounds like what you have is a "Tourist Card".
There is no need to stick this into your passport - just keep it with your passport when entering Cuba and during your stay.
When entering Cuba they will normally not stamp your passport itself (although they will if you ask), but will instead stamp the tourist card. When exiting the country they will collect the tourist card.
If you are an American citizen then you should make sure they do NOT stamp your passport, as Americans are forbidden from visiting Cuba under most circumstances. If you are from another country then there should be no issue if you get them to stamp the passport, even if you intend to visit the US in the future.