Connect the coax cable to an active wall outlet and then to the Cable In connection on your HD digital adapter.
(Hint: Not all in-home cable wall outlets are active. Try multiple outlets if the first one doesn't work.)
Connect the HDMI cable to your digital adapter and your TV.
Plug your equipment in to power and turn on your TV.
Using your TV remote, change the TV input setting to the proper HDMI input you used to connect the HD digital adapter.