When can I vote to delete posts?
Users with 10,000 reputation can cast a delete vote on a closed question, two days after it has been closed.
Users with 20,000 reputation can cast a delete vote on an answer with a negative score, and can vote to delete closed questions without the two day waiting period.
It takes at least 3 delete votes (or one moderator delete vote) to delete a post, more if it's a question with many votes. Note users with over 10,000 rep will see deleted posts answers (in red). More information is in the Privileges page for this privilege.
Why would I vote to delete a Question?
Generally we only delete closed, low scoring posts with no answers or poor answers. Closed posts are all "candidates for deletion" but generally only irrecoverably off topic/poor questions without useful information in answers should be deleted. If a post is more borderline but no attempt has been made to save it, you can either attempt to edit yourself or vote to delete it.
The two day waiting limit is imposed on 10,000 rep users so there's a window where the asker can edit and improve their question, or at least see why their post was closed. Even if you have 20,000 rep, consider waiting until the user sees what was wrong with the question.
Remember if a post is blatant spam/offensive garbage you should use a spam/offensive flag instead. Those get fast tracked for deletion, and may be deleted by a moderator/large amount of spam flags before normal-user delete votes take effect.
If you're looking to evaluate posts for deletion, use the following link:
Note: The date should be changed to two days ago when you run the search
Why would I vote to delete an Answer?
Comments or questions posted as answers should be deleted (and users without delete votes can flag these as Not an Answer). Additionally, any negative scoring answer can be deleted; if an answer really is thoroughly useless and does not answer the question ask asked, you may cast a delete vote.
The latter category is where community delete votes really come in; moderators generally don't delete answers because they are wrong or answering the wrong question, but only when they are extremely clearly not even close to an answer. As a rule of thumb, a moderator should be able to tell, with absolutely no domain knowledge (even if the moderator has relevant knowledge) that an answer is not an answer before they delete a post. See When should I flag an answer as 'Not an Answer'? for guidance on how to handle flagging answers.
However if multiple users vote to delete a negative scoring post, that's generally fine. If a post is a good example of a bad idea, making a useful signpost of "don't do this", consider leaving that post around. Otherwise feel free to cast a delete vote.
If you've voted to delete a question/answer consider dropping a link to it in chat so that others may review your decision and add their vote if they agree. If you're looking for posts up for deletion, see Most Delete votes (10,000 rep only). You can also see/audit recent deletions/undeletions.
What if I think something was wrongly deleted?
Bring up the post on Meta; bring a link if at all possible. All users with 10,000 rep can see deleted answers (or questions, if you have a link), so you can review deleted posts if you find them.
If you can vote to delete a post, you can also vote to undelete a post, unless the post was deleted by a moderator or spam flags (it will show a deleted by Community if it's deleted by flags). It takes as many votes to undelete as it does to delete.
You can also flag a deleted post (yours or someone else's) for moderator attention if you feel it's been wrongly deleted or if the post has been improved to the point you feel it's worth undeleting. Generally if a post was deleted by a moderator, flag it, if it was deleted by the community, bring it up on Meta or ask in chat if you're unsure why it was deleted.