Assuming that you are using a recent operating system on your Mac like Yosemite, Mavericks, Mountain Lion or Lion....and you have tested the long Ethernet cable to make sure that it is working correctly.......
Connect one end of the Ethernet cable to one of the three LAN <---> ports on the Time Capsule
Connect the other end to the WAN "O" port on the AirPort Express
Click the WiFi icon at the top of the Macs screen, and then click on AirPort Express just under the heading of New AirPort Base Station
When you click on AirPort Express, that will get the setup "wizard" running. It will take a minute to analyze the network and then display a window that looks like this, except that you will see your Time Capsule and AirPort Express.
Enter a device name that you want to call the AirPort Express. Mine is Express, for example.
Click Next and the window will change to look like the illustration below. Make sure that you see that the AirPort Express is being configured to extend using Ethernet.
When you see the message of Setup Complete.......click Done
And, you are done. Close AirPort Utility and enjoy your extended wireless coverage.