There's two ways to favorite something--
1) If you mean the Favorite Taxa thing that many people have on their profile pages, then that you get to by going to your Lists page. On the website in the upper right corner you'll see your username and icon, and when you click there a menu will pop up under it. Click on Lists in the menu and it will take you to your Lists page, which will have two default lists: your Life List (every species you've ever put onto iNat) and a list called Favorites. Any species you add to that Favorites list will show up on your profile page.
2) If you meant how to "favorite" (like a Facebook Like) a particular observation, then just go to that observation's page and look for the star icon and click it.
Cheers!