In order to enable Family Sharing your Steam Account, you will need to follow these steps:

• Open the Steam client and select “Steam” in the upper left.
• Go to “Settings”.
• From the "Family" tab, click "Authorize Library Sharing on this device".
• Be sure to enable Steam Guard on your Steam Account.
• Check accounts in the "Eligible Accounts" tab and choose the preferred one.

Requesting access from owner:

• Make sure to enable Steam Guard on your Steam Account first.
• From your Library you will be able to see games owned by other Steam accounts that use the same computer. Select a game and click "Borrow" to request access to that respective Library. Requesting access will send the game owner an email with a link to allow you to play games in their Library.
• The game owner will then need to click the link in the email to authorize your computer and grant your Steam account access to their games.

Here you can check how to enable Family Sharing your Steam Account: