Yes, but you need to first check with your current ISP as most/many do not allow web site hosting on their normal home user accounts.

One program you can use is called Apache. You can get it here http://httpd.apache.org/

Or if you got Windows XP Pro, then you can use Internet Information Services (IIS).
 
Installing IIS on Windows XP Pro @ Web Wiz Guide.

yesterday I found a button link to http://www.lighttpd.net/ in a bittorent search engine site. I haven't really tested it but it looks attractive.

www.no-ip.com will give you the name and site you have to make a page using what ever you want to use for example microsoft publisher or dream weaver macromedia than iis in xp pro will run it for you all the directions are on no-ip's web site how to set up a router to let in coming traffic in it was a little of a battle

no-ip is pretty sweet service. Depending on what kind of connection you have (Static or Non-static) the availibilty of your site will differ.
 
If you have static (your ip address never changes) you can choose either to give out the ip address as your web address or use no-ip's service to get a url. Your website is on as long as your computer is on and apache is running (assuming that's the program you use)
 
If you have a non-static connection (Your ip address changes every time you reboot your modem and/or pc). You now cannot give out an ip address, because it changes, but no-ip will solve that issue, because they have a free software that pings the server to tell them of an ip change if necessary, so your website will be restored within 5 minutes.
 
And finally, no-ip is free if you use a sub-domain. (ie. tugmistress.no-ip.com they have many master domain names to choose from so be sure to check it out).

Or if you prefer to keep things separate either:
 
Buy a router and another PC (specs depend on what your site is used for)
Or
Download a trial of VMWare and create a new virtual machine, build your site in the VM then run it using VMWare Player.
 
For either approach do some research on WAMP and LAMP. Again, depending on what technolgies your site needs (just HTML or PHP or PHP/MySQL etc.) WAMP/LAMP might be applicable. If not, just use IIS or Apache as mentioned above.
 
My separation theory might be useful to you as your main PC [potentially] won't suffer if something bad happens (like a security breach).
 
Personally I prefer Apache mainly due to it's ease of configuration however there are (of course) many pros/cons for each.
 
S

your post was very usefull...Now i've a dyndns account where my dynamic ip gets updated every 5 minutes, and i have a apachi server too.
I got a free subdomain www.meyya.dyndns.info from them and when you go through this address it takes to a service provider page in which my internet connection details are there and it also asks for username and password whicj i never set up for it.I have even placed my home in htdocs folder of apachi server.
Now tell me what should i do in order to connect my home page through the address ?