Instructions
Open the Steam website at Store.Steampowered.com and click the "Install Steam" link at the top-right corner of the website. Select the "Install Steam Now" link and follow the instructions on your screen to install Steam on your computer.
Sign in to Steam with your username and password after it's installed. If you don't already have a Steam account, click the "Create a New Account" button on the log-in screen to create a free account.
Navigate to the "Garry's Mod" page on the Steam store by clicking the "Store" tab at the top of the Steam window, typing "Garry's" into the search box at the top of the store page, pressing "Enter" and clicking the "Garry's Mod" option in the search results.
Click the "Add to Cart" button on the Garry's Mod page and follow the instructions on your screen to purchase a copy of Garry's Mod.
Click the "Library" tab at the top of the Steam window, right-click "Garry's Mod" in the list of available games and click "Install Game" to download and install "Garry's Mod" automatically.