When composing a document, whether it's an email to a friend or the next chapter in your own version of the Great American Novel, it's always a good idea to read through it for proofs and errors at least once before sending it anywhere. Even if you're sending it to someone like myself, whose job it is to proofread and/or copy edit your work for you, there's a lot of "pre-proofing" that you can do ahead of time. After all, as the author of your work, it's your job to "own" the work and have intimate knowledge of what your work is saying and how it goes about saying it.
One reason to proofread is that you may have blind spots while you're writing your piece, such as mistakes and misspellings that you commonly make while your brain is in creator mode and not editor mode. And if you simply read through the copy again your eyes will probably glide over many of those mistakes. It's important to put yourself into "editor" mode before reading through your work again and make your brain see the words and phrases individually.
One way to put your brain into editor mode is to use the "Find" function in whatever application you're using (MS Word, InDesign, Final Draft, Pages, etc.). This will help you see specific items that need to be changed, and your eyes/brain are less likely to glide over the mistake. For example, you want to make sure that a name you used in your copy is correctly and consistently spelled throughout the piece. Type the first two or three letters of that name in the "Find" box, then click on the button to jump to that name in the document, and so skip from name to name throughout the document to make sure each time it shows up it is spelled correctly.
If you KNOW that you have misspelled that name or word at least once, then type that misspelling into the "Find" box and use that to skip around the document to find all other instances where it may have been misspelled.
Maybe you're not sure you misspelled anything, but you know you put the apostrophe in the wrong spot. For example, in most current styles, one does not put an " 's " after numerals when describing a time period like the 70s. It should not be "70's." Though at one time it was common to do that and considered okay, now it's not. Now it's considered correct to write it as "70s" without the apostrophe. You want to make sure you have gotten rid of all those extra apostrophes. So, in this instance, you type the 's into the search box for the "Find" function. It will probably take you through to all the other instances where you have a possessive, as well as the numeral you are checking for, which will feel like a pain. But in this instance (as well as the others listed above), that's a good thing. It means you are being forced to spot check your document in a way that is making you read it out of order and pay attention to specifics. In this way, you will see the document differently and, most likely, find mistakes you weren't even looking for that happen to be in the same general area as whatever it is that you typed into the search function.
Of course, you still want to read through the copy one final time after that, because you always need to read it over one final time. That's just the way it is with proofreading.