I've heard there's a way to get questions reopened by doing something called a heroic edit.
What is it, how can I do it properly, and how does it help?
A heroic edit is any edits, or set of edits, that goes beyond the normal call of duty to help save a post from itself. They generally substantially revise a post to extract and make clear what, exactly, is so special about the post.
To maintain the quality and scope of a site, routine closures are a part of Stack Exchange. Closures are a way to signal from the community that a question has problems that must be addressed before it can accept new answers.
Stack Exchange is not a homogeneous community, and people do disagree. If a person disagrees that there's a problem with a question, they can vote to reopen the question (if they have enough rep) and/or convince other members of the community to vote to reopen. If 5 members of the community or one moderator is convinced, the question will be reopened.
If or when that fails, that's when the heroic edit comes in. By addressing the problems already identified by the closure, people will be more likely to be convinced that the question should be reopened.
Fair enough: you can try to keep looking for people who agree with your assessment, and can vote to reopen the question, to do so. But by taking other people's concerns with the question seriously and addressing them, you're likely to convince more people about the value of the post faster.
Copyediting is a relatively minor issue, and it's almost never the reason why a question gets closed. While improving the copy helps any post, it's unlikely to be enough to get a question reopened.
Posts can be closed for a variety of reasons: there is no single type of heroic edit that'll work for all cases. The goal is to address why the post was closed, so understanding why others closed the question is essential.
Start by looking at the close reason:
Then check the comments on the question, or check the meta-discussion site to see what people have said about it. Try to address those concerns as well in your revisions.
Finally, talk to the people who closed the question: they can explain what reservations they had with the question and help you address their concerns in your edits.
Not constructive covers a lot of issues. While talking with the people who closed the question can make the problems specific, there's some general advice:
Most really good heroic edits will attract reopen votes quickly and automatically. You can also flag it for moderator review or post the question in chat to see if you can get others to reopen the question.
Not all questions can be saved, even with the most heroic of edits. Other times, people still aren't convinced the issues have been addressed. If you think the question should be reopened and talking to individual people hasn't made that happen, open up a question on meta to discuss what—if anything—can be done to get the question reopened.