Once you've finished your story and your hero has prevailed, sit back for a minute and congratulate yourself. You've accomplished something great--getting a complete story down on paper from start to finish. Now the work starts!
It's funny, but when I go back to read something I've written after letting it sit for a while, I'll catch myself saying "Wow, did I write that? It's good," in some places, and "Ugh, how could I write that?" in other places. That happens all the time and it will happen to you. As you reread, take notes by either writing in the margin of your manuscript or adding them on your computer. You may find that a certain scene does not work, or a subplot might be a little dodgy. Be on the lookout for plot elements that aren't wrapped up or characters that drop out of sight without explanation. Once you've identified these things, go back and fix them or get rid of them if they don't move your story forward to its conclusion.
After you've done that, read it through again to see if there's anything else that needs fixing or clarifying and rewrite it. Then, keep an eye out for any typos or misspelling or punctuation errors. You can edit this as you reread the first time, but I find that when I do that I am not paying enough attention to the plot points. If your prefer, you can proofread for spelling and punctuation before you reread and rewrite.
Finally, once you've got it as polished as you think it can be, find someone whose opinion you really trust and ask them to read it. Ask them to tell you what they think. Did everything make sense? Was the pacing good? Were all the loose ends tied up?
In many cases, it's not unusual for thee rewriting and editing to take longer than it actually took to write the first draft. But that's good, because once you've taken your story through the entire rewriting and editing process, you can be sure your story is as good as it can be.