Can I simply attach to the Time Capsule with an Ethernet...
Yes, you would connect an Ethernet cable from one of the LAN <-> ports on your existing wireless router to the WAN port (circle icon) on the Time Capsule.
Use AirPort Utility - Manual Setup to configure the Time Capsule
Click the Time Capsule tab just below the icons to assign a name to the Time Capsule, a device password, and and adjust Time Zone settings
Click the Wireless tab next to the Time Capsule tab and change the settting for Wireless Mode to "Off". It is a good idea to do this if you have another wireless network already set up, since there may be wireless interference problems created if you try to use two wireless networks in close proximity.
Click the Internet icon, then click the Internet Connection tab
Connect Using = Ethernet
Connection Sharing = Off (Bridge Mode)
Update to save new settings and be sure to restart the entire network again. That should get you going.
You will be able to backup to the Time Capsule from your Mac using either the wireless network that you have now, or you can connect the Mac directly to one of the LAN <-> ports on the Time Capsule to establish a direct connection. I would recommend the direct connection for the first backup, since everything on your Mac will be copied over to the Time Capsule and this will go much faster using an Ethernet cable.
Once you have the initial lbackup completed, you could use wireless for subsequent back ups since they will only take a few minutes each time they occur.