Proofreading your own work is harder than proofreading someone else's, and there's a specific reason why: you already know what the sentence is supposed to say. Your brain fills in missing words and skips over typos because it's reading your intention, not your actual text. The fixes below work by breaking that pattern.
This is the single most effective trick, and also the most skipped. Reading silently lets your eyes skim ahead and your brain autocorrect. Reading out loud forces you to process every word at speaking pace, which is exactly when missing words, doubled words, and awkward phrasing become obvious — you'll physically stumble over the sentence that isn't working.
Your brain partly recognizes text by shape and pattern, which is part of why familiar mistakes hide in plain sight. Changing the font, increasing the text size, or switching from screen to print (or vice versa) disrupts that pattern recognition and makes your eyes actually look at each word again instead of gliding over the familiar shape of the paragraph.
Start with your last sentence and work toward the first, treating each one in isolation. This breaks the narrative flow that normally carries your attention forward, so you're checking each sentence for whether it's correct on its own — not whether the story makes sense, which you already know it does.
If you have the time, the single best edit is to step away for a few hours — overnight, if the deadline allows. Coming back with fresh eyes recreates some of the distance an outside reader would have naturally. A piece proofread immediately after writing it and a piece proofread the next morning are, in practice, being read by two different versions of your attention span.
Most writers have a handful of mistakes they repeat — their/there, a missing comma before "which," doubled words when they revise a sentence mid-thought. Keep a running mental (or literal) list of your own recurring errors, and do one pass that searches specifically for those, rather than trying to catch everything at once.