So how do you share your library with a friend? Unfortunately, one of the big drawbacks is that you will need to have logged into your Steam account onto your friend's machine at least once.
Let's say Alice has a game that Bob really wants to play. Alice needs to visit Bob, log in onto Bob's computer with her Steam account and then authorize Bob's computer.
Many believed that you can request authorization via Steam profile pages but that is unfortunately not the case. There is an option to request access via email, but again, the person you'd want to borrow a game from needs to have to logged into your machine before. It may be possible to circumvent being physically present by using a remote desktop application such as TeamViewer.
When you log on your friend's computer, you are asked to enter Steam Guard password and also you can name your friend's computer for better recognition.
Authorizing is done via the Manage family sharing & devices menu, that can be found under Steam > Settings and Account tab.
There you can see all accessed computers and here you can also authorize or deauthorize machines. Here you have screenshot where This Computer is my main machine and computer named Crystal belongs to my friend and he has access to my steam library.
So you managed to gain access to your friends library and now you are wondering, where are the games and how can I play them? Remote libraries are stored in the main Library tab on the bottom of your game list. Games from all libraries are counted so expect number in All Games to rise considerably, but games that both parties own are not shown in remote libraries.
Now you can just pick a game and start downloading it just like it is yours. When games owner wants to play something from his library, you will be given 5 minutes timer to leave the game and notified by Steam overlay notifications every minute. After this period game is forcefully ended (we are suspecting some sort of process killer performs this task).
The library owner is also notified who is currently accessing his library, but the notice is not intrusive and is only shown in list view as a single line:
Unfortunately the sharing recipient will be kicked from game A even if library owner will starts playing game B. This rules out any kind of way of sharing a game and playing multiplayer through Steamworks.
Currently it is possible for more the Steam library owner to play at the same time as the sharing recipient by switching Steam to Offline mode. That way you can play game from all libraries that are in your computer without interruption. It remains to be seen whether it's possible to have both parties connect to a non-Steamworks multiplayer service, e.g. a Quake III dedicated server.
There are indications that this process change in the future, and that the game owner will be able to set more refined rules what games you can access. The SteamOS page states: "Soon, families will have more control over what titles get seen by whom, and more features to allow everyone in the house to get the most out of their Steam libraries".
We yet do not know how third party DRM games will behave exactly (Uplay, GFWL games) but they are also shared in the library. We suspect that you will need a new account (and therefore to purchase the game individually) for this to work.
Update: Uplay and GFWL games are protected by CD-Key that will be shared with your friend. Steam library is being updated and these games should not be shared anymore, however some low profile games still can be shared.
Do not share your library unless you've claimed (started playing) all your third party and CD Key protected games.
Update 2: Beta participants can share their libraries with ordinary users, but ordinary users can't share their libraries back.
Be sure to come back for updates as we are still researching this new feature or visit official guide at Steam Support page.
Many thanks to user Crystal for assisting with testing.