How much reputation do you gain for upvotes in questions or answers? How much rep do you gain for different types of badges? Is there a place that tells you all this?
All of the general reputation information can be found in your site's
/faq, linked at the top as "faq". The specific section can be found here.
The primary way to gain reputation is by posting good questions and useful answers. Your peers will vote on your posts, and those votes will cause you to gain (or, in rare cases, lose) reputation:
- answer is voted up --------> +10
- question is voted up ------> +5
- answer is accepted --------> +15 (+2 to acceptor)
- question is voted down ---> -2
- answer is voted down -----> -2 (-1 to voter)
Badges do not earn reputation - all you earn from accomplishing the specified task/objective is the badge itself. Apart from these, the other main things to expect of reputation are bounties (which are elaborated in a proceeding section of the faq, and are a method to award extra reputation on answers), and offensive/spam flagging (if an answer or question is flagged as offensive or spam by 6 users, it will be automatically deleted and will penalize the post author by 100 reputation).
You can find an even more in-depth analysis of the full reputation system on Meta Stack Overflow's Reputation FAQ.
In the faq at https://english.stackexchange.com/faq, there is a section titled 'Reputation'.
It's not obvious but under the 'show more' link, it will display all the information Grace showed and more details, like what abilities a certain reputation level will get you.
This is the case for all SE sites; they used to have this sort of detail immediately visible on the faqs, but they changed the deisng slightly recently to hide details requiring a link visit to see them.