Downloaded games and apps through Steam is usually a one-time occurrence, save for the occasional updates. It's a good thing, too, because some games can push 100 GB in size, if not more.
For those of us who now have to worry about data caps from our service provides, the task of moving a Steam library to another computer can be the cause of overages and unnecessary charges depending on how many items are in your library.
Steam offers a method to backup your current library with relative ease, so long as you have a spare drive big enough for the backup and a couple hours to kill.
Before you get started, make sure all apps and games are up to date. If not, the first thing that will occur after restoring from a backup is the download of updates.
With everything updated, click on Steam in the top left corner, then select Backup and Restore Games.
Next, select Backup Currently Installed Games, then check the box next to each app and game you want to backup. Choose a location to store the backup, then give the backup a name (ignore the CDROM option below the text field).
Once you've started the backup, leave the computer to do its own thing. Depending on the size of your library, it can take a couple of hours to complete the process.
To restore your backup on a different computer after installing Steam and signing into your account, connect the external drive, select Steam > Backup and Restore Games > Restore a previous backup > select the location of your backup > pick the apps or games you want to restore.
After the restore process has finished, all of your settings and progress should be intact. It may take a bit of time, but likely no longer than the time it takes to download a game from scratch and you don't have so stress about your data cap.