The longer you work on writing something, the easier it is to miss spelling and grammar mistakes that quickly stand out to a second pair of eyes. But since it's often difficult to find someone with time to proofread, consider having your computer read it out loud. TextEdit's speech function (which you can find under: Edit > Speech > Start Speaking) and Google Translate (from English to English) work well for this. If you can bear listening to the robotic voice, you'll start to uncover typos that you'd have likely missed otherwise.
For example, have you ever read over an email only to find that you included a clumbsy "the the" after you'd sent it? Somehow these types of mistakes start to blur together when I read them visually, but when I listen to them they're nearly impossible to miss.