Is there some special formatting that I need to do?
Yes, the USB drive needs to be formatted in Mac OS Extended (Journaled), also known as HFS+. To find out how your USB drive is currently formatted, connect it directly to your Mac, and the hard drive icon should appear on the Mac's desktop. Right-Click on the hard drive icon, and then click on Get Info. Look for Format to see how the hard drive is currently formatted.
Once the hard drive is formatted correctly to work with the Time Capsule, you can connect it to the USB port on the Time Capsule.
Note 1......the USB port on the Time Capsule is a very old, low powered design, so you may find that you need to use a powered USB hub connected to the Time Capsule with the hard drive connected to the powered hub.
Note 2.....the USB port on the Time Capsule is an old USB 2.0 design. Chances are, your new hard drive is a USB 3.0 design. USB 3.0 is supposed to be backwards compatible with USB 2.0, but this is not always the case.
Note 3.....the hard drive connected to the Time Capsule will act like a separate drive. You will not be able to combine the 1 TB Time Capsule with the new hard drive and have the two drives act as one large hard drive.