For the U.S, you will most likely have to take an English test firstly. You would then take the SAT's or the ACT or something of the equivalent.

Here is an MIT application link for international students.

https://gradadmissions.mit.edu/applications/international-applicants

Every college has different procedures and standards so find it on their website. However, it should be semi-similar to this MIT page. You can check with the U.S immigration website to get the correct forms.

https://www.uscis.gov/

You may be subject to a waiting time, so best do it as soon as you can. However, find what you need first on the college's website that you want to go to.