Once you complete your graduation(preferably science or arts), you can apply for post graduation or masters course in Deccan College at Pune or MS University at Baroda. These are the two best institutes catering to field archaeology in India. If you want to do it abroad, you can appear for the GRE exam to secure scholarship in any well known university in USA or UK which are the most sought after countries to study archaeology. Voracious reading is one of the most important requirement of this field.
Best of luck For your future :)
You would most likely major in anthropology with a focus on archaeology. Your advisor will make sure you take all of the classes you will need to complete the degree. Aside from anthropology classes, the degree usually requires some distribution in history, sociology among some others. Now, if you want to become an professional archaeologist, you would probably want to get a masters and maybe even a Ph.D. after your BA is done.