Before other people sharing your computer can access your Steam library you'll need to authorize the device and their account.
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 Family
To authorize the device you're currently using select Authorize this Computer
Once authorized you'll be able to select which Steam users you want to grant access to your library. The list will only contain accounts which have logged into Steam using that device.
From now on if an approved account 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. You can return to Family tab within the settings menu at any point to view which account has been using your library and when.
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.