You need to determine the services you'll provide (web site, ftp, email, etc.) and estimate the amount bandwidth you'll need along with hardware and software requirements.
You need to register a domain name with a registrar. There are many registrars. Their fees vary considerably, but all are for an annual period. Personally I use
GoDaddy.com. You will also need a DNS services provider once you know where your domain will reside and its IP address.
There are hosting companies who will provide complete turnkey setup and some who provide little more than the hardware and a limited amount of software for your domain. Bare bones providers offer only rack space for your own hardware and an internet connection.
The technical side of managing a domain consists content creation and presentation design, knowledge of the software and similar tasks for managing a server remotely. Typically you will not have physical access to the hardware.
The legal requirements vary depending on jurisdiction. In the USA you must provide certain personal information to register a domain some of which becomes public. Here is the information returned from a
whois inquiry:
Your email address
Your name
Your street address
Your city
Your state
Your postal code
Your country
Your telephone number
The bottom line is that setting up a domain from scratch is not a trivial project for the novice.