It's extremely hard to proofread your own work! I've worked as a freelance writer for years, and have nobody else to edit or proofread my work. I'll ask my husband, son, or sister (who's an editor) about wording an awkward sentence if I get stuck.
But what I usually try to do is finish a piece of work before the deadline and put it aside for a day and try to just put it out of my mind. Or even for a few hours. Then I go back to it and re-read it "word for word." It's amazing the things I'll catch! The thing is, when you write the material, you know what you want to say, and what you've written "says" it--whether or not it really does. Going back to it with a fresh, objective eye can make a big difference. You can not only catch typos, but you often catch a badly worded sentence, a misspelling, or a usage you look at and think, "Gee, that doesn't seem right. I'd better look it up."
I look things up every single day, and I've been a writer for more than 30 years. I look up spellings that don't look right (amazing how many words look wrong when they're right), and I look up rules of grammar when I've forgotten one or when I'm asked to write per a style or style guide I'm not familiar with (APA, for example).
I learn something new every day, but not everyday!
I've learned to never trust spell-check or my phone's auto-fill feature.