I started mine (www.origamimark.co.uk) by getting an internet service provider (ISP) who provides hosting services. I use Plusnet, who seem to be about the best all round at this sort of thing. They provide 250Mb of web space, I then bought a domain name, which Plusnet hosts for me.
I then created some simple content to test (HTML and some Java applets), following ISP online help pages (PlusNet provides lots of documentation to help), and hey presto - a web site. PlusNet then socialised my web address among the search engines, so it can be found.
PlusNet support PHP and MySQL, so I have since learnt PHP (a scripting language) and MySQL (a database), and now the website content is mostly stored and generated from the database. This means I can change the content through screens rather than writing more code.
You can buy fancy software like Dreamweaver for website development and maintenance, but so far I have managed just fine with a free editor (PSPpad) and a file transfer program (Smart FTP Client).