How can I apply for studies abroad?

It is quite difficult to put the entire admission procedure in one answer but I’ve tried to include all the necessary points.

First of all, you need to have a bachelor's degree with good scores. Each university has a specific minimum percentage requirement which you need to check from their website before applying.
Official Transcripts of your Bachelor’s program are to be submitted to the faculty. A transcript consists of all the courses you've completed in your Bachelor's program. Typically a GPA of 3.0/4.0 and above is okay.
GRE- Graduate Record Examination: It's a test for all the students aiming to pursue any graduate courses within the US. Mostly the very best Universities have GRE as a compulsory requirement to get into the MS courses. However, there are a few universities that don't require GRE, so you can consider that option also.
If you are an international student, English Proficiency is an additional requirement that is to be completed before applying to the MS courses. These exams are required because English is the medium of instruction in US Universities and English proficiency tests help in checking the understanding of the students. The two exams that you can consider for English proficiency are- i) TOEFL (Test of English as Foreign Language): it is a web test, divided into 4 sections: Speaking, Reading, Writing, and Listening of 30 marks each. A score above 100/120 would be sufficient; ii) IELTS (International English Testing System): Many Universities also accept IELTS instead of TOEFL for the English Proficiency requirements. If you decide which Universities you'd wish to apply to beforehand, please check their requirements before choosing which test to opt for. IELTS is additionally divided into 4 sections: Reading, Listening, Writing, and Speaking. The result is within the type of bands (out of 9) for each section and a mean band score. For MS, a band score of above 7.0 is safe with individual bands above 6.5 depending upon university requirements.
Statement of Purpose(SOP): it is a 1-2 page essay that describes why you'd wish to be a part of the particular course and why you're the right fit for it. All Universities have different word limits for personal statements so make sure you check the specific word limits while applying.
Letters of Recommendation: the faculties under which you've studied can write these letters and submit them.
Passport and Visa: these are your actual tickets to apply to any university abroad, goes without saying.
These are pretty much all the basic requirements and procedures for admission to MS courses in foreign universities.