I read an article about IP addresses that are needed before I can host my own website. I do not understand how to get my own IP address.
I use Ubuntu 11.10.
check out full tutorial here
As long as you can currently connect to the internet, you have an IP address. Most likely it is a dynamic address which changes every time you connect your system. In order for other computers to be able to find your website, they need to be able to get that IP address. If you have your own domain name, you would want to have a DNS entry so people can use http://www.mydoman.com or whatever to translate to your IP. For this, you would need to use a service such as DynDNS to update your DNS records every time they change. Or you can arrange with your ISP to provide a static address for you so it only needs to be entered into the DNS system once (normally when you buy your domain name).
Some notes about self-hosting in general:
You should not run your web server on a machine that gets used for other purposes.
Your web server should run as few services as possible at all times.
You should apply all relevant patches to the server as soon as they are available.
If your router supports it, your web server is best placed in the DMZ.
You should check various hardening documents for Linux servers such as the one here: http://www.freesoftwaremagazine.com/articles/hardening_linux I don't necessarily agree with the author's "always compile yourself" rule depending on the source of the software. In most cases, if it is available in the repositories, it has already been compiled with the most useful options and for most uses, it does not require recompilation.
Hope this helps.