Open Steam and sign in on the computer that has the games
Click Steam in the top-left corner
Select Settings
Go to Family
Enable Authorize Library Sharing on this computer
Select the user accounts you want to share with
Have the other person sign in to Steam on the same computer at least once
Repeat the authorization process for each account and computer you want to allow
Make sure Steam Guard is enabled on your account
Log out and let the other user sign in to access the shared library
Note that only one person can use a shared library at a time
Note that some games are not shareable
Note that DLC may not always be shared