Is this possible?

Question

I would like people to be able to fill out the form online and be able to save the completed form as pdf to their home computers.

Answer 1

you must send (submit) the form data to server side, handle the creation of pdf on server side (with php as you tagged it), and send a response to the client with a html page with a link to download the created (dynamucally generated) pdf...

obviously, you need to make the pdf temporary, as you could overflow your host capacity limit by saving unlimited number of files at server side ^^