No piece of writing is good without a proper round (or three, or ten!) of editing and proofreading. Ideally, someone else will polish your writing, but even then it's advisable to give your own work another check. Whether it's your own work or someone else's—I've gathered some tips to help clean up written words and listed them in no particular order.
Know the rules
Be sure to have a glossary or set of instructions or rules for proofreading whenever necessary. This is especially important if you read other peoples' work. Know which spelling is preferred (UK or US English, old or new spelling), how characters are named, and what kinds of issues to look out for.
Be consistent with those tags
While writing, make it a habit to always place tags in the same way (e.g. with a space either BEFORE or AFTER a highlighted term).
<PAColor0xFFf3d900> word <PAOldColor>
I prefer to connect the tag with the word since it might be followed with a punctuation mark and I can do an easy search for punctuation marks to see if I added a space too many. Being consistent in your work makes spotting mistakes easier.
Know which mistakes you frequently make and beware of homophones. Words like "they're", "their", and "there" get mixed up way too often.
Write drunk (if you must) but edit sober
The famous quote that might or might not have come out of the wise mouth of Mr. Hemingway carries a timeless lesson. Some say that not being quite there opens one's mind and therefore can help spur one's creativity. While I might argue with how well I can write under the influence, for doing a good editing job, I can't have my eyes jumping from line to line, forget the beginning of the sentence while I'm in the middle, or read three lines at once. Non-sober, everything I read may make sense—or no sense at all. If you claim you can proofread well while being in the sky with diamonds, I bow to thee, but I might still not feel confident asking you to proofread my work.
Get in the zone
Turn off unnecessary distractions, meditate for a few minutes or go for a quick run—whatever helps you clear your head. Do what you got to do and then focus on the work at hand. If you feel like your thoughts are drifting off or in case you get interrupted, read the sentence or section again.
Unfamiliarize yourself with the text
If you have the time, take some days after translating or writing the text and between every round of proofreading. Getting some distance to the text will help you see it with fresher eyes.
Print those files
Get back to the roots and work with pen an paper. We often learn and understand better when reading something on paper rather than on screen. At the very least, with our faces planted in front of screens for most of the day, working with paper is a nice change of pace.
Change the font
Anyone who has ever worked on a piece of writing for a while knows how hard it is to edit your own work. Every word looks so familiar that you can't be quite objective anymore. By changing your writing's font, you trick your brain into thinking that you are NOT reading the piece you just wrote or read 226 times.
Run a spellcheck
The integrated spellchecks offered by your office software or the CAT tool of your choice provide only a limited level of correction and sometimes make suggestions that are blind to context. However, while they cannot distinguish between "Bear with me!" and "Beer with me!", they will tell you when you type a word that the program doesn't know, which might mean the word does not exist.
Question every word
Don't assume that anything you read is right, be it in grammar, spelling, or content.
Read, re-read, then re-read again
Find your own rhythm for a workflow. I suggest you read a sentence fluently, then read every word, then read the whole sentence again.
Revise your revisions
If you change part of the sentence, read the whole sentence again. No exceptions. Make sure this change stays within consistency of the text, or adjust the other texts accordingly if necessary.
Don't be yourself
Dress up and pretend to be someone else. This one works the same way as changing the font.
Get up, get out
Try proofreading from another spot than usual. Do you usually work sitting at your desk? Try working at the kitchen counter, the living room floor, the hallway stairs, that cute café across the street, a library, or the city bus.
Mind the details...
...but keep the big picture (e.g. the style) in mind.
And if you have the time...
This is only a small number of many possible strategies for proofreading. Would you mind sharing one of yours?