There are several ways one could study abroad. Also it is a well known fact that in abroad countries there is much less competition than India, but then again it is highly costly too.
This is why students from India apply for scholarships so that The Indian Government or any other private institute could fund them. Spending your time to study abroad is a transcendental experience as you get to know the other cultures of the world. Before picking any country to study think about the cost (tuition cost + living money) and also about your overall safety and welfare.
There are some countries like Australia, Canada, US, UK and Germany that offer student exchange program for one semester in their top universities.
To begin with, think about the course you want to enroll in (there are a plethora of courses) and the university that will help you study. Since English is not your first language you will have to apply for
TOEFL - Test of English as a Foreign Language test. It is a standardized test to check the English speaking and writing abilities of a non-native speaker. There are many documents required for the submission before you want to enroll in the university, do keep on checking the notifications at their particular website. Here is a list of some general documents that might come handy at times -
Passport photos for identification
A statement of purpose
Academic references/ letters of recommendation
Certificate and transcripts of your secondary education
Proof of English-language proficiency (e.g. a TOEFL/IELTS certificate, for schools in English-speaking countries), or other language test
Admissions test results (e.g. GMAT/GRE results, for graduate programs)
There are chances that you may have to apply for student visa for that keep visiting the desired university's website as they will give you detailed information about the documents you must carry.
Also stay in touch with the Indian Embassy as there are several procedures of living in an entirely new country, which is in itself is exciting.