This is super common and a mainstay of any repair shop. Open up your phone and follow a guide to take out the logic board. The port is attached to the logic board.
Ports are pretty simple things---investigate it to see if you think it could be stuck back down with a soldering iron. If so, give it a shot.
If the port itself is damaged, then you'll need to replace it. This will depend on your skills. One of your local repair shops will be able to do it for you, or you can use a mail in service. If you have good soldering skills, it is something you can DIY--find a YouTube video and try it. Samsung s3 charge port is the beginner job of cell phone soldering.
However, If you are new to soldering, you will probably tear off a pad and that will complicate the soldering on of a new port---then you'll have to send it to a specialist like me to a complex charge port soldering job.
Best of luck, but either way this is definitely a solvable problem!