From Lifehacker–Connecting an Ethernet cable between your Mac and one of the Ethernet ports on the AirPort Time Capsule is definitely the fastest way to back up your data.
This step-by-step walkthrough from Apple’s official help forum explains how to get your backup working:
Connect an Ethernet cable from one of the Ethernet LAN <-> ports on your main router to the WAN port (circle of dots icon) on the Time Capsule
Open AirPort Utility 5.6 and click Manual Setup
Click the Time Capsule tab just below the row of icons to name your Time Capsule, assign a device password and adjust Time Zone settings. (You can use the same settings that you used previously if you want.)
Click the Wireless tab and change the setting for Wireless Mode to “Off”
Click the Internet icon, then click the Internet Connection tab
Connect Using = Ethernet
Connection Sharing = Off (Bridge Mode)
Update to save settings and wait 25-30 seconds for the Time Capsule to restart
Connect an Ethernet cable from your Mac to one of the LAN <-> ports on the Time Capsule. Turn off wireless on the Mac.
You are now ready to backup using Ethernet
Once the first backup is completed, you can make all future backups automatic, which will only target files that have changed on your Mac since the last backup was performed. At this point, using WiFi shouldn’t be a problem as the backups will be much smaller. If any readers have a similar setup at home, let CC know how you went in the comments section below.