Favorite questions are marked by clicking the star below the question's score. It is searchable by using the `infavorites:<user>` query (where `<user>` could be `mine` to search your personal set of favorites).

Favorite tags can be set in the prefs tab of your user page. Again, you can use [intags:mine](http://mathoverflow.net/search?q=intags%3amine) to restrict a search to your favorite tags.

For more details see: 

* [How do favorite questions work?](http://meta.stackexchange.com/questions/53585/how-do-favorite-questions-work)
* [What do "favorite tags" and "ignored tags" do?](http://meta.stackexchange.com/questions/19173/what-do-favorite-tags-and-ignored-tags-do)