1, click on the top left corner steam, open the Settings page
2. Select "Home" in the Settings page and click "Authorize this computer" on the right.
3, then you will be successful in your computer to share the game.
4, after others user account login steam can see and play to your own library of the game.
How to authorize playing other people's computer games
If you see your roommate's account with a game you want to play, you don't have it, then you can want them to send a shared computer authorization request, and once authorized, you can access, download, and play their game in the Steam Library.
Steam Home Sharing FAQ:
Q: Do I authorize a shared library of devices or friends to have a maximum number of caps?
Yes. You authorize up to 10 devices to be used for home library sharing, and you can authorize up to 5 accounts on all your authorized computers to use your game library.
Q: Do I have to be online while playing a shared game?
Yes. You must be online to access and begin to play the game shared to you.
Q: Can I share a particular game, or can I only share the entire library?
Shared and borrowed is the entire library.