Every writer should learn how to edit their own stories. It is hard but the more you write, the better you become so don't worry about being the greatest writer right now. Just learn as you go. That's how we all get to the top! Again, writing should be enjoyable. The more you know, the better you get! This is something all writers must face, even the great writers like Stephen King, Judy Blume, and even Dr. Seuss when he was alive.
Before you begin editing, make sure you finish writing your story. That way, it's all there. Don't try bouncing back and forth (write, edit, write, edit). Stay in one mode until you're done, then change and work on the next level. Once you're a pro and you will get there, then work the way you like. Right now, you need to learn. (This may not work for everyone so if it doesn't work for you, ignore me and edit the way you want lol. Just do what works best for you!)
Reading your story aloud will help you catch more mistakes than reading silently in your mind. Don't read off the computer screen, it can hurt your eyes. Print it out and then read it. If you stutter while reading it, there's something wrong. If it doesn't make sense, there's something wrong. Fix it and continue. Keep moving forward until you have read the last page. Now begin the writing stage, filling in those mistakes. Once that's complete, read and edit. Continue until you're done! Never settle with "its good enough". You're better than that! If you're lost or don't know, ask for help. Get a Beta Reader but don't depend on them, learn to do this yourself.
Make sure your characters have the same name through the entire story. Mark doesn't become Matt halfway through the story and he's the same person. That's why keeping notes can be helpful! It keeps it all sorted.
You also want to make sure you look at all the endings of sentences (.!?). Make sure they fit the sentence. Commas and Semicolons too! Ans check for quotation marks " ". If there's one in the beginning, there should be one at the end. Same thing goes for parentesis ( ) too.
If you have chapters use stars ***** to show the end of the chapter and begin the next chapter on the next page. Check to make sure that's correct. Spell out the number in this case.
Using "Beta Readers" can be a helpful tool. 3 is better than 1. A beta reader is someone who will read your story and make suggestions to improve it, electronically or printed. Writers are good choices but you should always use someone you trust. And just because someone says you should fix something doesn't mean you have to. This is your story; you get the last word in the subject. Just listen to what they have to say and tell them thank you, whether you make the change or not. Get used to this because when an editor from a publisher tells you something, it will be for real. Don't say yes to everything and don't say no to everything. Saying no will cause the editor to stop working with you on other books. No one wants a hard writer to work with so compromise sometimes. No one is out there to steal your work so don't be paranoid all the time. If you can afford it, you can also pay an editor to help you but try to learn as you go. Reading books on the subject is always a good idea.
There's no rush so take your time when you sit there and look over your work. During your first few stages, no one will be looking it over after you're done so don't be afraid to mark up the pages with a red pen or pencil. As long as you can read your own writing, make the changes directly on the manuscript. Then when you go back to make those changes, everything is in front of you saving prescious time which you really need anyway!
When you are finally done with all the editing, had someone read it (hopefully 3 people you trust or more), and edited a little more; you're ready for the publisher/agent search. Don't forget to get started on that next book though. You must never stop writing, no matter what stage you're in on this book (or the next book). Good luck to you!
Joining writing groups is beneficial, especially at this point. Editing is harder than writing a book. It takes courage because you have to be strong enough to face your mistakes. Everyone will make them. If there isn't one in your area where you live, start one. And there's also groups online so don't forget about those. Check out the Resources page here to find other websites to help you. Forums are a great place to start.