Hi Akalya,
it is a very easy process to obtain one. First off, you will need your baby's birth certificate. Once you get that, go to this web page that has all the informations for applying for new passport:
http://travel.state.gov/passport/passport_1738.html
The application form is available on this website. You will need two passport size pictures of your baby, which you can get done at walgreens or longs or any other studio. You can send the application fee in the form of your personal check.
Once you are ready, locate one of the passport processing centers that is closest to you , using the above website. For minors, it is required that both parents be present while turning in the application for passport. Other wise you will have to get a no objection form ( also available on the website) and the respective spouse to sign it.
All this information is also given on the passport web site.
Hope this helps
Vandhana