How do you get a stuck doorbell to work?

That depends on what kind of doorbell it is. An electric one or mechanical one.

If it´s mechanical you need to open it and remove residue between the parts. It is also possible the spring (if it has one) is broken. But most likely the bell is just dirty and the dirt stops the bell from working. So open, clean and oil.

If it´s electrical you need to check if all the wires are intact. Electronic bells are not easy to repair if they get broken. But just like the mechanical bell, there may be dirt somewhere on the button, so cleaning that might help.