Hello.

As an Indian engineering graduate, you have to prepare for GRE and TOEFL examinations. Without these, your applications will be rejected straight-away. 

After getting good scores in these examinations, you can visit the websites of the universities where you want to apply. Fill the application form, and pay the fee (usually $95-$105). Then you will be notified if you get selected.

Different universities have different way of selection. So be prepared for interviews and next-level tests.

Usually, coachings are not required. But you can take one for GRE, as it is very important exams for engineers if they want to apply outside India.

All the best!