I want to set up the web server at my home. I already have registered for the domain name. I do not want to use hosting services. How should I set up the Apache and the settings with the registrar of the domain name so that my site is up and running?
Please note that hosting at home is disallowed in the Terms of Service by many Internet Service Providers, and some may even disconnect you for this or charge fines.
If you are allowed to home-host according to your provider's terms of service, you should set up a webserver (from your question I already see that your choice has fallen on Apache) at home which runs on your public IP (usually you will need to forward port 80 in your router to your server's internal IP). The installation of Apache differs per operating system. For an easy Apache installation under Windows, I would recommend XAMPP, available at: http://www.apachefriends.org/en/xampp.html
Next, you should point your domain's A record to your public IP. (Hopefully, your ISP provides a static one, which many ISPs which allow home-hosting do). It is recommended to also do this for the www. subdomain.
If you are using Linux, the easiest (but not the best) thing to do is install Apache (and Mysql/PHP if you want dynamic) then install Webmin as this will give you a nice interface to everything.
If using Windows, Try downloading the Web Platform Installer which should get you installed with IIS, SQL Server, ASP.Net (and I think PHP) Very quickly.
Next step would be to go to your DNS records and set an A record for your domain that points to your IP, and a Cname that points to your domain.
Lastly, you want to forward port 80 on your router to the machine that has the webserver.
That should be it! If you do not understand any stage, please say in comments and I will be happy to help.
A WAMP, or LAMP, depending on your OS, should install everything needed for a website. You then point the DNS at your IP (You DO have a static IP address, right?) and everything should go ok.