Search for "Compact Flash Reader" on Amazon and buy one with good reviews. Expect to pay $15 or less.
With the GPS off, eject the memory card by pushing on the little button next to it. Put the card in the reader and plug the reader into a USB port on your computer. Run the Jeppesen Distribution Manager application, and it will automatically detect you have an update available and will ask if you want to update your card. As a sanity check, verify that the Jepp Distribution Manager is pointing to the correct drive.
When you click the 'Update' button on the Jepp Distribution Manager, do NOT pull out the compact flash card or disconnect the reader from the USB port until you get the message saying it is finished.
Now simply take the card back to the GPS and plug it back in. When you start it up, it will show the new database start and end date during the startup routine.