There are no exposed screws on the Time Capsule, and it’s just like Apple to go that way if they can:

You must peel off the rubber pad on the bottom of it.  I periodically used a razor blade to give the adhesive a chance to peel off with the pad.  Some people have suggested using a hair dryer to warm up the glue before peeling it off but I didn’t and it came off pretty nicely for me anyway.  This exposes all 10 of the screws:

When you remove the bottom of the case be careful because the fan is connected to the bottom pan and must be disconnected via an easy-to-unplug connector:

The hard drive is actually held into place by the rubber grommets that sit down into the bottom pan of the Time Capsule.

Before you attempt to lift the hard drive out make sure to disconnect the hard drive’s temperature sensor.  Look for the twisted wire that comes up and around the drive.  I was able to peel it off.  Lift out the drive and disconnect the power and SATA cable.  You will now need to remove the “slugs” that are screwed into the bottom of the original drive and transfer them onto the new drive.  The rubber grommets may have stayed on the slugs–simply put them back in their holes in the bottom pan.  Connect the new drive’s power and SATA cables and place back into the time capsule and reconnect the temperature sensor.  Reconnect the fan and then reinstall the bottom pan.  I was able to get the rubber pad to stick back onto the bottom without any problem.  After booting up the Time Capsule it detected the new drive, formatted it, and it showed all the new space: