Since your TV is HD you will want an digital tuner with HDMI out. A "converter" box is usually SD only and doesn't have HDMI.
The antenna connects to the tuner. The tuner connects to one of the HDMI inputs on the TV.
When you turn on the box it will ask you to scan for channels. You can only tune in channels stored in memory so if you reorient the antenna you have to run the scan again to see if you got any additional channels. Some will be stored in memory but be too weak to produce a reliable picture, You usually delete these from the scan manually.
There are tuners with built in DVR functions. There are some with dual tuners too.