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Here is the most common way of doing it.
To get a form working properly, you need to install a CGI (Common Gateway Interface) script on the server on which the site will be hosted. Those scripts are mini programs that will handle the job. Those programs are usually written in PERL (a programming language).
There are many PERL sripts that are available for free out there and are quite easy to customise. They come with all the instructions. Best way to learn is to use your favorite search engine and search for PERL scripts or CGI srcipts to find huge libraries of those. Go and get your hands dirty! It's fun! :)