Reading your draft looking for mistakes is very important – so much so that you should be doing it a lot, in a number of different ways.
Once you are happy with a draft, use the spell and grammar checking functions of your word processing program. This can be a really useful way of picking up some mistakes. However, that doesn’t pick up everything, as sometimes you write a word that is a correctly spelled word, but it just isn’t the word you wanted. Unfortunately the computer doesn’t know which word you wanted (not yet anyway), so there are other ways of proofreading that might be useful:
Read your text out loud. Yes, you might feel stupid doing that, but the brain functions slightly differently when reading out loud than when reading in your head. Reading out loud can help you pick up mistakes.
Give the text to somebody else to read. Actually give it to two different people – one who knows about the subject, and one who doesn’t. Both will be able to help you with spelling or grammar, but also they will be able to tell you whether your text makes sense, both to an expert and a non-expert.