Instructions
Launch Steam on your main computer and ensure the game you want to install is present in the "Library." Boot your laptop and navigate to steampowered.com.
Click "Install Steam" on the upper-right corner of the screen, then click "Install Steam Now." Run the installer and follow the prompts, clicking "Launch Steam" at the end.
Select the "Library" tab and choose the game you wish to install. Click "Install" and wait until the process is complete, then click the game in the Steam interface to play without a CD key.