In the Steam client, click on the Games menu at the very top, and then 'Activate a Product on Steam'; after you hit next a couple times in the window that pops up, there will be a place where you can copy the alpha/beta key gotten from the Larian Vault, which will add it to your library. After that, you can click on Library in the Steam client, select Divinity Original Sin from the games list and then click the Install button (or right click the game name and select Install Game).