Requirements
1) PC with Windows OS
2) XPort/XSata or a Transfer Kit
3) XBox 360 Hard Drive or Memory Card
4) XPort360, XPlorer360 (Optional)

Steps
1) Make sure the correct drivers are installed for XPort 360, no driver is needed if you are using a Xbox 360 Hard Drive, but there are drivers you need to install if you are using a Memory Unit, the drivers should come with XPort 360.
2) Once all the drivers are installed. Just plug in your XPort, XSata or your transfer kit, and then launch XPort360 or XPlorer360, I would have to recommend XPort 360 if you are not to familiar with XPlorer360.
3) Launch XPort 360 or XPlorer360 and then click, File, Open HDD or Memory Card. And then select your device. Once the device has been loaded fully, you should see Partition 3, open that. Partition 1 is just your Cache for faster loading times on your Xbox 360 and Partition 2 is for Xbox 1 Compatibility.
4) Click Content in Partition 3, you will see 0000000000000000 and another one or more with random letters and numbers, those are your profiles, 0000000000000000 is used by the system, so you dont have to worry about that.
5) Browse through all the other profiles, if there is only one other one, then just skip this step. Once you browsed through all profiles, decide which one is yours by choosing the one with most/all of your games in it.
6) From there, you can just click and drag all of your favorite game content to your desktop for backup, or if you want to transfer games from another HDD (requires a JTAGed Xbox 360, or a Dev Kit depending on the file type)
7) Enjoy!

Extra
If you are using a memory unit, just do the same, except go to Partition 2 instead of Partition 3, the Memory Unit's do not have Xbox 1 Compatability which removes a partition.