A client asked me to add a form to his page he needs the data that will be received from the form to be put into a database, I want to know if this kind of work is rather normal, or if I should charge him extra money for it.

I am new at this, please!!!!

That's pretty normal for a lot of web development. Extra is a matter of perspective. I suggest finding some who can do it for you or do some serious studying. php and MySQL are popular options for storing information from a form in a database.

I consider to be the basic knowledge for any website coder.

I agree. That's like developer 101. However if you're a designer and not a developer it would make sence to possibly not know it.

Although it is basic knowledge for a developer, I may still change extra for it. Not much though, as it would be a very quick job.

I would highly consider outsourcing to a third party form provider who actually backs up the data. formsite and logiforms are both great. I guess it just depends on the client.