Some areas of the game may allow you to rent things. In most places, you will be able to figure out how to do this by reading the posted signs, or by conversing with the locals.
Most innkeepers will respond positively to polite inquiry, such as "Sir, I'd like to rent room 12, if you please."
If you've already rented a room from an innkeeper, you can simply hand them some more money to extend your rental time.