Formal:
* ¡Abra la puerta, por favor! (Open the door, please!) - This is the most polite and formal way to make the request.
* Le ruego que abra la puerta. (I beg you to open the door.) - This is even more formal and implies a sense of urgency or need.
Informal:
* ¡Abre la puerta! (Open the door!) - This is a direct and casual command.
* ¿Puedes abrir la puerta? (Can you open the door?) - This is a more polite and less demanding way to ask.
* Abre, por favor. (Open, please.) - This is a shorter and more informal way to say "open the door, please."
More casual:
* ¡Ábrela ya! (Open it now!) - This is a more demanding and impatient command.
The best way to say it will depend on your relationship with the person and the context of the situation.