You probably have a single IP (mostly dynamic) address assigned to you by your ISP. You should get a dynamic domain from any of the dynamic DNS providers. The service is free and you can register upto 5 domain names (atleast with dyndns.com). The most popular is www.dyndns.com
but there are others, which you can easily find using google.
Regarding multiple websites, I assume you have a single IP address so you would be using name-based virtual hosting...which is basically same ip address resolved for different domain names. This is then resolved to different web server directories that you have created. Each one would have their own content. This is easy to setup if you follow the how-tos and tutorials.
Once you have setup your website, you would then need to constantly watch out for ip address changes. If you dynamic dns entry goes stale, your website would be unreachable. This should be taken care off if you have one of those new routers with dyndns option. If not, then you can use ddclient
which constantly watches out for ip-address change and updates your dyn dns record. This way your site is reachable almost all the time.
Very good tutorial worth checking out is www.linuxhomenetworking.com
Hope this helps,