And do NOT entrust this process to a computer spelling or grammar check. A spell check picks up spelling errors, not usage errors and typos. A grammar check is only as good as whoever programmed it and often makes no allowance for grammatical grey areas and unique voice expression.
Our favourite proofreading trick is to read the piece out loud, preferably to someone capable of providing feedback on what they're hearing. While time consuming, reading out loud will highlight all the typos and misused words/phrases. You'll also suddenly hear all the awkward passages and unnatural sounding dialogue and numerous other things which slip under the radar otherwise.
We guarantee the time taken to read out loud will be worth it in the improved quality of work.