Note that this stuff was covered in another section of the guide. This section was created to make it easier for people to find.
Once you reach level 80, you’ll have the opportunity to work on your elite specializations.You’ll need to obtain quite a few hero points (250 per spec) to complete these specializations or even get them to a usable state. If you’re completing the story in order, it’ll take a while for you to complete these, since core game Hero Challenges only grant one hero point each. In Heart of Thorns and Path of Fire, they grant ten each and there are often hero point trains running through Heart of Thorns zones to help people complete them all. Hit “Y” and use the LFG tab to find them. Drubid has a solo guide for those who would rather do this without the aid of a group. For a list of all hero point challenges, use this wiki article.
If you play WvW, you can use your testimonies of heroics in exchange for hero points.
Mastery Points section here