Allot of users do that the admins of the forum how do they do that
I want to start my own forum so users can register to my forum and pay a fee

Well, you know, nowadays, most forums on the net are free, and if people know that this or that forum is not free, you can expect them to look for another forum.

Secondly, if you want to run your own forum, you can learn how to make a really good one (using programming which I don't know how to do), then perhaps you'll get members, or you look for a site hosting forums for free and gain popularity before applying fees.

But then, you might as well lose all your members all at once... I think the ideal would be to make your forum popular, and allow members to donate from their free will. If you host your own forum, you'll need money to keep it up on a server and if the income does not exceed the monthly (is it monthly?) fee, then you'll not make profit in the way you want.

What would be the purpose of this forum? What reason would someone have for signing up for it?

Creating a forum isn't hard. There are canned forum packages you can purchase or use on a subscription basis. Applying a secure login (meaning a person would have to pay for an ID to enter) is also not that difficult. I'm sure you could find examples of code on the Web.

But getting someone to pay for a service that a lot of places offer for free is not going to be easy.

My favorite free, and easy to use forum is Simple Machines. Check it out here:
Home of SMF: Free PHP and MySQL forum software (http://www.simplemachines.org/)

For easiest installation, scroll down to the bottom for the Webinstall option.

... of course you'll need a server to put it on. For basic hosting, I recommend Lunarpages (http://www.lunarpages.com).

I agree with all of the above... its easy to create a forum... whats difficult is making money off it. Or getting it to get good Search engine placement so others will ever find it.

You can either cowtow to advertizers... or go subscription... but to get people to separate with their money, you really need something compelling enough for them to want to pay for. And if you don't get enough paying members to make sufficient posts what members you have will leave.