Getting your question re-opened is going to end up being a popularity contest while having to confirm to the rules of this Stack Exchange.
So your question is closed, you've made the edits and want to get it reopened. The magical number is 5 reopened votes, and getting those votes is hard.
First thing is that make an edit will move it to the top of the Active page. Here users who are interested in your question, can go in, have a read and vote to re-open it. If you have a popular question that happens to attract the attention of many people, it gets reopened faster. People see your question. Read it and vote to re-open if they want to. To this end, having easy to read, well formatted and shorter questions will likely get opened faster, because it wont take as much effort to get through everything.
The second way is through the review queue. There are several queues for users with a lot of points which make it easier to users to moderate questions and answers here. Your question will be placed in the re-open queue and any people who are reviewing will see it there as well. To that end, you still need to have a well formatted question because lets me honest. If you see a wall of text you might just skip the review and leave it to the next person.
Finally, I believe Moderators can open a question which was unfairly closed. This can happen sometimes, but usually happens the other way when someone asks a clearly inappropriate question and a Mod closes it straight away. This is going to be rare, and sometimes, bringing it to the attention of meta can help get the required attention to open your question. However do not expect this to happen.