From your home timeline, hover over the Tweet you'd like to favorite.
Click on Favorite, a gold star will appear in the upper right hand corner of the Tweet to confirm that you've favorited the Tweet.
You can also favorite a Tweet from a user's profile page and a Tweet's permalink page.
Note: If you mark Tweets as favorites from users with protected profiles, the update will not appear in the Favorites tab on your profile page unless the viewer is an approved follower of the update's author.
To undo or remove a favorite:
Hover over the Tweet you favorited, you will see a gold star in the upper right hand corner and Favorited on the Tweet.