There is an Instructable here for adding a USB port to an Xbox controller but I haven't seen one for putting it in a memory card to leave a controller alone. I had a dead memory card plus some spare female USB ports on a dead hub so this was born.
Step 1: The Parts and Tools Needed.
First things first, tools and parts needed.
Solder with flux (I use flux core; works great)
knife or something to trim plastic with
screw driver (most likely a phillips head)
Xbox memory card, preferably a dead one (duh...)
female USB port
wire, preferably color coded
Optional tools and parts I didn't use for this:
hot glue gun (for giving structural support to the port)
heat shrink tubing (protect against possible shorts if your solder joints aren't nice and small...)
Now we're ready to start. I didn't photograph the tools since they're common stuff...
Step 2: Gutting and Cutting the Casing.
Now we can get into it. First you need to open the memory card and desolder the Xbox memory card PCB from the controller port connector. I did this by getting my iron nice and hot then dragging it across the pins rapidly several times. (Not best method but it worked...) Make sure you note the orientation of the port in casing to prevent mistake of getting it backwards later. (Like me...)
With the casing open you can now proceed with fitment of the USB port. Put it anywhere you like as long as it clears the controller. I prefer the very end to keep everything symmetrical and for ease of access. Take your time when cutting. Measure plenty; cut once. You don't want to make the hole too big and have it loose not to mention it looks terrible...
Step 3: Wire It All Up.
Last big step is to wire it up. This was simple enough to do. There are plenty of diagrams for the pinout of both the Xbox memory card port and USB connector. Just Google them. If it makes you feel safer, you can put heat shrink tubing on the wires before soldering them to cover the connections in case of possible contact with other wires resulting in a short and possibly damaging your hardware. You can also use hot glue to glue the port in the casing for better strength. I didn't need it since the casing closed tightly around the port and holds it in place firmly.
Step 4: Done.
One final note: you won't get the full 500 mA of current that regular USB sees from the memory card ports so a HDD that uses USB power only is out of the question. Most USB flash drives will work. This includes plenty of SD cards through adapters as well. If there is no driver needed for it in Windows and it is 4 GB or less, chances are it'll work on the Xbox.
Here's a video demonstration using a HDD: