Before other people sharing your computer can access your Steam library you'll need to authorize the device.
Authorizing a device can be done by opening the Steam Client and clicking on the Steam
button located on the menu at the top left. Once you have the menu open click on Settings
Mac users will need to choose Steam
and then Preferences
from the applications menu at the top of the screen.
From the Settings page select the Manage Family Sharing & Devices
Once you've clicked on the button the Authorized Devices
window will appear. To authorize the computer you're currently using select This Computer
from the list and then hit the Authorize Device
You'll then be prompted to give your computer a name.
Once you've clicked Ok
the computer will be authorized for Steam Family Sharing. You can return to this screen at any point to view which account has been using your library and when.
From now on if any user logs into Steam from the device you gave authorization to they will be given access to play games from your Steam library if it's not in use.
Other users using an authorized device can view your library by using the filter tool near the top of their games list and selecting your username.
Steam libraries can be accessed by one person at a time across all devices. If you're playing a game from somebody's library and they begin playing a game themselves, you'll receive a notification stating you have a set amount of time to exit your current session.
As the account holder you'll always have priority access over your library.