Voting to reopen
You must have the "view close votes" privilege in order to vote to reopen your own question. Users with the "cast close and reopen votes" privilege can vote to reopen any closed question, not only their own. On established sites, these privileges are awarded at 250 and 3000 reputation points, respectively (beta sites have different thresholds).
If you have the appropriate privilege, you will see a link near the bottom of the question (on the same line as "share | edit | flag") that you can click:

Clicking on this will ask you to confirm that you want to vote to reopen this question. If you cast the first reopen vote, your question will be added to the Reopen Votes review queue so that others can see it quickly and possibly cast more votes. After five (5) votes, the post will be reopened.
In some cases, a single vote is enough to reopen the question:
- A single vote from a moderator can reopen any question closed for any reason immediately.
- Questions closed as duplicates can be immediately reopened by a user with a gold tag badge for any of the question's tags.
Comments to reopen
Leaving comments about voting to reopen does nothing in and of itself. You can try and address a specific user who may have left a comment as to why they voted to close and ask them to help cast reopen votes if you think they voted in error.
You can also leave a comment asking for other users to vote to reopen if you've edited your question to a better form.
Editing to reopen
If the comments are helpful as to why the question has been closed, you can edit the post so that it's a good, on-topic question, or to explain why it's not a duplicate. The close reason, while not always accurate, should point you in the right direction of what to fix.
Editing the body of a question after it gets closed will also add it to the Reopen Review queue, where people with the the ability to cast reopen votes will assess it. A question can only be added to that queue once per closure via editing, and won't be added if it's been more than 70 days since it was closed or if you flagged or voted to close/reopen the post prior to editing it.
If the question is edited, reviewers will be shown a diff view of the edit by default. For this reason, you should make sure that any edits after closure should make clear why the question should be reopened. If you or someone else makes a minor edit and doesn't follow up with a more major edit, reviewers may only see the minor edit and thus disagree with reopening, which may force you to resort to the next option.
Requesting on meta to reopen
If you've tried the above options but it wasn't reopened, or you can't vote to reopen and it's been more than 70 days since the question was closed (so you can't edit it to have it reviewed), you can make a request on the per-site meta tagging it support reopen-request.
You should only do this if:
You tried the above three options and users still disagreed with reopening it, which you can verify by clicking the clock symbol on the left side under the voting and bookmark buttons to access the post's timeline, then looking for any completed reopen reviews.
You can't exercise any of the above options (e.g. because you don't have enough reputation to vote to reopen and you can't have it reviewed via an edit because it's been more than 70 days since it was closed or you previously flagged the post before editing it).
Clearly explain why the question should be reopened (why it's a good, on-topic question, or why it isn't a duplicate). This is also a good way to obtain further clarification about why your question was closed.