Since you have asked about a free Web hosting service provider, it would be a little tougher to find one. You may find a lot of sites that allow you to build your site free of any charge. But, being free - they lack in certain functionality. Besides, such services offer low bandwidth and low disk space. The customer service will also be not much reliable.
However, if you are just starting off it would be a better idea to opt for a free service. You can always migrate to a paid service once you begin getting decent traffic.
A couple of such free Web hosting services include -
1. Hostinger.com
It provides you a disk space of 2000 MB. It supports around 50 scripts and a free website builder.
2. Indiagetonline.in
This is a collaboration between Hostgator and Google. It is aimed at getting the smaller businesses online by providing necessary support. It offers you a free .net domain and free Web hosting for one year.
Please note that with the free Web hosting services,you will not be able to get a own domain as in www.yoursite.com , instead you get a customised domain name like www.your site.provider.com.
Live....and Let Live!