Reema, I think the fastest way is to immerse yourself. If you are coming to the US for your Masters (congratulations on deciding to get a graduate degree, and for going to a western university) then just come early. Come now. Hire a tutor or language teacher here. Big cities all have language schools, and you will be with other students. (Many foreign students spend a semester in a language school before starting their college work.) In your first semester of graduate classes, start with a light course load, so you can have time for more English study. Your written English is excellent but you will get more confidence by speaking!

I recommend watching CNN, TV series (Big Bang theory, if you want to learn legal english - the Suits, and so on). You can also try writing short formal text messages (memos, formal letters etc.)  for native speaker to check them and correct if necessary.  As you can see I'm not perfect in English, especially I still have some problems with grammar. But, watching TV series helped me with quickly creating basic sentences. Ah, You can also try google translator to make translations and then trying to improve them, so they don't sound awkard. I found it, as a quite a challenge. ;)

A possible way to help would be to watch American TV or videos on youtube of Americans talking to each other. I can help too, as I would like to learn a few arabic words as well. Good luck!

Thanks for commenting.

You can only learn vocabulary once you start using them in sentences, else you try to memorise soon you will forget them. Speaking like native English speakers is an art, first you have to listen properly and try to  imitate how they deliver sentences and words. For that first you need to find yourself which English accent and dialect suits you and you are comfortable with. Listening I would say is the best practice to pick correct pronounciation of the words and pick up the commonly used phrases initially. And in different areas different phrases are being used. Hope this will you inshAllah.