How to access self-powered USB hard drive connected to Airport Time Capsule

am not clear on how to access the space on the hard drive and/or files stored therein through the Airport Utility.

You don't use AirPort Utility to access the data on the hard drive, you use AirPort Utility to see whether the drive is recognized. It will be if the drive is formatted correctly in Mac OS Extended (Journaled) or FAT32. The Mac format is strongly preferred.

In the example below, you can see that the hard drive on my Time Capsule is named Backups.....(the drive on your Time Capsule is likely named "Data", unless you have also changed the name...... and another USB drive attached to the Time Capsule.....named 500 GB Drive

So, the first check that you need to do is to make sure that the drive is recognized using AirPort Utility.

To access the data on either the Time Capsule hard drive or the attached USB drive......

Open any Finder window

Double-Click on the Time Capsule icon under the Shared heading on the left panel of the window

Another window will appear with a Connect As button, click on that button and enter the admin password for the Time Capsule

The name of the Time Capsule drive and the USB drive will appear in the next window as folders

Double-Click the folder of the name of the drive that you want to open

I believe I've followed Step 1 correctly (example below)

No, you are looking at a Time Machine window. Please note that I asked you to check using AirPort Utility. Please follow the steps above (and again below) very carefully.

Open AirPort Utility on your Mac and check to see if you can see two drives. One of them will be named "Data" and the other will be the name of the USB drive.

In the example below using AirPort Utility......you can see my two drives....."Backups" and "500GB Drive".

You will see "Data" and the name of your USB drive....if the Time Capsule recognizes it. Using AirPort Utility, please report on whether you see both "Data" and the name of your USB drive.

In other words, if the Time Capsule does not recognize the USB drive, you won't be able to use the drive until it does.

I do not see the 1TB external hard drive that is plugged into TC via the USB port.

If the USB drive does not appear in AirPort Utility, there is an issue somewhere. Did you check using the first step above?

You don't use AirPort Utility to access the data on the hard drive, you use AirPort Utility to see whether the drive is recognized. It will be if the drive is formatted correctly in Mac OS Extended (Journaled) or FAT32. The Mac format is strongly preferred.

In the example below, you can see that the hard drive on my Time Capsule is named Backups.....(the drive on your Time Capsule is likely named "Data", unless you have also changed the name...... and another USB drive attached to the Time Capsule.....named 500 GB Drive

this external HD is what I had been using with Time Machine to backup my iMac for some time.

Time Machine backs up differently to a "local" drive that is connected directly to a Mac compared to a "network" drive like a Time Capsule. You won't be able to connect the USB drive to the Time Capsule and continue to back up using Time Machine unless you start over again with a new backup to the USB drive.

Time Machine backs up to a "local" drive connected directly to a Mac go to a normal folder called Backups.backupdb. Time Machine back ups on a "network"drive like a Time Capsule go to a special container called a sparsebundle. The two different types of back ups are not interchangeable.

In other words, when you connect the USB drive to a "network" drive like a Time Capsule, the USB drive becomes a "network" drive as well. It won't act like a "local" drive again unless you reconnect it to the Mac.

I previously used a 1TB external hard drive (self-powered, connected to my iMac via USB).

If the USB drive does not appear when you check using AirPort Utility, it is possible that you may need to use a powered USB hub with the drive when it is connected to the Time Capsule.

Reason......the USB port on the Time Capsule is old (and slow) USB version 2.0. Your USB drive is likely USB 3.0. USB 3.0 is supposed to be backwards compatible to USB 2.0, but the theory does not always work in practice.

In addition, the USB port on the Time Capsule is not a high powered port, like that on a computer.

So, a powered USB hub might work better as far as USB 2.0 / USB 3.0 compatibility.....and.....the higher power supplied by the USB hub might help make up for the low power provided on the Time Capsule port.

Finally, some drives simply won't work with the USB port on the Time Capsule. I don't know why. If you have tried a powered USB hub and the drive still won't appear when you check using AirPort Utility, then you may one of the drives that simply won't work with the Time Capsule's ancient USB port.