Since you already know something regarding domain, bw, space and stuff. I shall not talk more about it.
If you want to build a complete new website on your own, you will need some tools and knowledge to help you.
Tools needed: Click here
, scroll down to post #3 under HTML & CSS Editors
Knowledge: HTML Tutorial
After which you should be able to build a pretty nice and simple looking site. You can also make your own graphic designs etc.
However, with all the above, you are only able to make static site which means the website looks the same all the time. If you want dynamic website, then you have to learn server-side language such as PHP/mySQL.
Hope this information helps!