Step 1: Materials
-An unused Xbox 360 hard drive
-The Hard Drive Transfer Kit cable that came with the 120GB hard drive
-A disk format utility for your pc (this tutorial will use Windows Disk Management)
Step 2: Plugging in the Hard Drive
Step 3: Formatting the Hard Drive
Scroll down to the large black "Unallocated" block. (Make sure that it's your Xbox 360 HDD; its size should closely match your hard drive's size.) Right-click that block, and select "New Simple Volume".
Keep clicking Next until you reach the screen titled "Format Partition". You can keep the file system as NTFS, but I would recommend changing it to FAT32. You can also change the Volume Label if you want.
Click Next, then Finish. The drive will format.
Step 4: You're (almost) Done!
(Additional notes: Unfortunately, the hard drive won't be recognized by the Xbox 360. However, it will be recognized on a PS3.)