Someone may give you a free phone, but you still have to pay to have it connected. 
You really sound like you need help, so I suggest you forget doing it alone and sign up for a server such as Zarconia. I use them, they are excellent and they will install Dolphin for you. I'm not sure of the rates, but you can find out here:
https://www.zarconia.net/
If you insist on doing it alone, here's basically what happens. The fact that you have name servers, means that you have dome part of this already:
- Download Dolphin - Free
- Download and install an FTP client - considered essential. I use WINSCP
- Choose a hosting Service provider. They need to supply the following in their hosting package:
 - MYSQL
 - PHP
 -Apache
 - A Control Panel (Can be CPanel)
 -Service (Dolphin is quirky and needs certain PHP functions to be activated.)
- Obtain a Domain name (Sounds Like You've Done This)
 - Go to your control Panel and enter your Name Server details and Domain details.
 - Wait 48 hours for the Domain to appear on the Internet.
 - While on the Control Panel, select PHPMyAdmin and create a database. Remember the name,      username and password..
 - Check regularly by typing http://mydomainname.com or whatever.
 - When you see a page saying the domain exists, you are ready to boogy/
- Open WINSCP and FTP (copy) Dolphin to the Home Directory of your server.
- Enter Http://mydomainname.com again and a Dolphin splash page should appear. It will ask you to install Dolphin.
 - Do the install using the database name, user and password you created above.
 - Set up a Cron Job
 - Dolphin should now run.
 
 
Or for a few dollars someone at Zarconia will do all this for you and more!
E.A.O.E (Errors and omissions excluded.)