How can I copy/transfer games via external hard drive?

Steam supports backup-files. Here is a part from the Steam FAQ/How-To's:

Creating Backup Files

1. Right-click the game in the Library section
2. Select Backup game files...
3. Check the boxes for any other games to backup at this time
4. Click Next >
5. Browse to the folder where you wish to create the backup files (the files will be stored in c:\program files\valve\steam\Backups by default) and click Next >
6. Select the Backup file name and set the File size for the media you plan to use.
7. Click Next > to begin the backup process.
8. Once complete, choose Open backup folder to move or burn copies of the backup files

Restoring from Backup Files

1. Install Steam and log in to the correct Steam account (see Installing Steam for further instructions)
2. If the backup files were copied to a CD or DVD, the process should run automatically when the disc is inserted. If not, run steambackup.exe from the disc
3. If steambackup.exe is missing, please download this copy of steambackup.exe and place it in the correct backup folder.
4. Continue through the Steam windows to install the necessary games.

Alternative to the Backup Feature for Third-party Games

1. Go to your \steamapps\ folder (by default, this folder is located at C:\Program Files\Steam\steamapps or on 64-bit systems, C:\Program Files (x86)\Steam\steamapps)
2. Locate any .ncf files for the game.
3. Locate this game's folder in the \common\ folder.
4. Copy all of the .ncf files and the game folder to a disc or available hard drive for reinstallation
5. For future installations, copy these files and folders to your new Steam installation.
6. Make sure to place it back in the proper folder (\steamapps\ for .ncf files and \common\ for game folders). In addition you may also rename/delete your ClientRegistry.blob to force Steam to rescan your gamedirectory.
7. Re-start Steam and you may see a small download to confirm the newly identified install.

For additional information read the complete article I linked below :)

Source: Steam FAQ/How-To's and Steam Glossary ClientRegistry.blob

All you should need to do is simply start Steam, then sign into a Steam account that owns the game. As long as it's in the Steamapps folder, Steam should see it and let you play.

Alternatively, if it doesn't show up on your steam list (happens to me on a friends computer) then find the game and download it and before it tries to download it fresh, it will check for existing files and boom - it'll find what you copied.