SMF For Free Support Forum

Oh, may I ask you, when someone makes a forum, how do you make that domain appear. Do you have to pay?

No..  its available to everyone.
Admin > Domain Manager

Do NOT do anything in there, fill anything in,  press any buttons until you have purchased a domain name, created the nameservers with them, pointed them to the IP number provided in Domain Manager etc.    If you do your forum will become unusable.

No because, how do you sort of get a thing with yourname after.

Like with me it'd be www.Sitenametitles.alert.com?
And, how do you "Host"?

Do a Google Search for Domain Hosts
Or use Godaddy.com to purchase a domain name as I said

The domain name can not contain two dots (.) in it as the one you posted has.
It has to be for example:     somename.com,  somename.net,  somename.org,  etc

IF you are talking about self-hosting the forum -  going with a host, installing the software and running it yourself instead of using a forum with this service - we can not help you with that here, nor will we provide answers to questions about that here.  You will have to go to simplemachines support forum to find out about all of that  (easily found via google)

forum urls with this service are that way as they are sub-domains and the naming denotes the server they are located on  (smfforfree.com, smfforfree2.com, etc)   You can not change the url.  You can buy a domain name  (thru a domain host) and park your domain on your forum as I said earlier.

As to who owns the net?    (its not Al Gore)  lol..... read this or do a Google Search for "Who Owns the Net"  You will find tons of information.
http://computer.howstuffworks.com/internet/basics/who-owns-internet.htm
Brief timeline of the internet:
http://www.webopedia.com/quick_ref/timeline.asp

To park on your SMF for Free forum?   No.   It will not work.

As I said a few posts back -  the domain name can not contain two dots in it... it has to be somename.com, somename.org, somename.net, etc. 

we are getting way off topic