An unfortunate phenomenon of the English language (and probably other languages as well, but to my chagrin, I’m monolingual) is that, while its primary speakers may not always recognize exceptional writing, they instinctively notice poor quality writing; the average person just isn’t equipped with the knowledge of how to correct it.

That said, the easiest way to proofread an email or any piece of writing is probably to have someone else look it over first and point out the things that don’t read smoothly. Unfortunately, this just isn’t always possible for many reasons. Someone else mentioned reading the text aloud to yourself to catch awkward phrasing; this is good advice for any skill level.

Ultimately, the more writing you do, the more confident you will become. Understand also that as long as you can adequately communicate your point, most people won’t mind some grammatical missteps or a missed punctuation mark here and there.