Stack Exchange is collaboratively built, maintained, and moderated by the community. If you see a question and you disagree with the stated reason for its closure, you should first try to edit the question to improve it as much as possible. Read the close notice and any comments carefully to address concerns raised there. Any question with significant edits that address the close reason(s) are automatically put into a review queue to be considered for reopening.
You can leave a comment on the question itself calling for it to be reopened. Be detailed: explain why the question shouldn't have been closed; don't just assert that it should be reopened. Be constructive: name-calling is against the Code of Conduct, and is more likely to drive folks away than to win them to your cause. Remember, anyone on the site with at least 3,000 reputation points can vote to reopen a question – even if a moderator closed it.
Be sure that you've read the close notice and any comments on the question so you can address any concerns raised there. Addressing the concerns often means editing the post, which any user may do.
If a moderator (a user with a ♦ symbol after their name) closed the question, then you may flag it for moderator attention. Again, do this only after editing and include a detailed explanation of why it should be reopened. There is more than one moderator, and moderators do reconsider their decisions.
If you have at least 3,000 reputation points, you can vote to reopen the question yourself.
If you're simply unsure about the validity of the closure, the best place to ask is on the community's meta site. Asking in the meta site allows those who took the action to comment, and will help others to learn about the issues being discussed. You can find a link to the site's meta in two places in the site's top bar: under the "help" menu (the question-mark icon) in the upper right, and in the Stack Exchange site switcher (under the Stack Exchange in the upper right.
Reopening a question follows the same process as closing a question.
Users with 3,000 reputation can cast up to 50 reopen votes per day. When a question reaches 5 reopen votes, it is no longer closed, and new answers may be submitted. You may only vote to close or reopen a question once. To cast a reopen vote, click the "Reopen" link beneath the question.
Moderators may close or reopen any question with a single vote.
How do I find questions that someone thinks should be reopened?
There are two tools to help questions with reopen votes get more attention from users who have the ability to reopen them.
Review. There are a number of review queues to help with different aspects of community moderation; one of these is a queue for all questions with reopen votes. Any question that has received one reopen vote gets added to this queue, as well as any post with significant edits that address the close reason(s).
Tools. Commonly referred to as the "10k tools", this page lets users with at least 10,000 reputation points see even more information – reopen votes, delete votes, migrated questions, and other information. The important one for this is the "Close" tab. Here, you can see questions that might have been closed incorrectly.