There are a number of ways to add games to your games library:
In the Browse section, by hovering over a game card and clicking the ‘heart’ icon.
From other people’s game libraries, by hovering over a game card and clicking the ’heart’ icon.
From the game page itself, and clicking the Like Game button.
In your profile’s Overview tab, and clicking the Add Game button (this will also add the game to your Pinned Games section).
And finally, in your profile’s Games tab, by selecting which Tag folder you want to add your game/s in and then clicking the Add Game button.