When proofreading your work, avoid the temptation to multi-task.
1. Read your paper out loud first. Listen for grammar errors, or things that just don't "sound right". Highlight these and check them carefully to make corrections.
2. Check for spelling mistakes. You can use the grammar and spelling checker for this.
3. Double check the grammar issues raised by your grammar and spelling checker.
4. Finally double-check your citations and quotations. You can use find and replace for this.
But looking at one thing at a time, you are less likely to feel overwhelmed and can address one issue at a time.
This video from the University of Sheffield gives some good tips on how to deal with common errors in punctuation, spelling and grammar.
This video from Edith Cowan University covers the top 10 editing and proofreading tips.