Word, then line, then sentence
An important part of editing is being able to de-construct your writing. You must begin by seeing each word independently. Work in paragraphs, looking at each successive word, scanning for spelling and grammar problems. Then lift your focus to the sentence, reading each sentence as a whole, watching for inconsistencies and errors. Then read the paragraph as a whole, once again looking for errors.
Simple Grammar
The key with grammar is to keep it simple. Master the correct use of the apostrophe, comma and speech. This trio will allow you to produce a workable manuscript with few grammatical errors. Don’t be tempted to use more complex grammar (no matter what Word suggests!) unless you are confident with its correct usage.
Does it feel right?
When reading your work you are looking for the bits that don’t feel right. If a section is a bit off or you have to go back and re-read a sentence then you have a problem. Also look for jarring, if a word or phrase doesn’t fit then follow your gut and change the section.
Plot
Keep a track of the key aspects of the plot. If you say your main character was born in London, make sure you don’t later talk about his early life in Liverpool. If you tell the reader a side character has a wife called Sue, make sure it doesn’t later become Mary. Readers (and agents and publishers) WILL notice the smallest plot errors.
Third party reader
Ask a trusted friend to read your work and make (constructive) comments on the page as they read. You can then go through the document and find the bits that didn’t read right. If a reader is picking up a section of plot that doesn’t make sense, your response should not be to explain verbally but to re-write the section so it is clearer.