To have HDTV mirroring on the Rezound you need to first buy an MHL adapter, they range in price from $12+ online, to HTC's own (which comes with an HDMI cable, too) being $40. Note that most of these adapters use micro USB (you not only need to have the adapter plugged into the TV, but also have the adapter plugged into a wall charger to supply power, or it won't work right, but this also charges your phone, which is cool.) so you will also need a micro USB cable, too.
The MHL adapter mirrors your screen on the TV, menus, everything. I've noticed some sluggishness when doing some things, like playing games, but that might be my adapter (some of them vary in performance, mine is a really cheap one.) You sadly can't turn the screen off, and between the screen being on, and the processing power needed to do this undertaking can make the phone very hot (at one point mine was pushing 120 degrees.) Turning down the brightness on the phone's screen all the way (which doesn't affect the brightness on the TV.) will somewhat alleviate this.
The neat thing about MHL vs other HDMI out ports on some phones, is that if your TV is MHL compatible (pretty much any decent HDTV made within the last year is.) then you can control aspects of your phone with the TV's remote, like menu surfing, using the gallery, etc. I sadly haven't had a chance to test this out, since neither mine or any of my friend's TVs are new enough to feature MHL.
As far as image quality, it looks really nice, played some HD movies I had on my phone and they played perfectly, some of the colors may look odd to you, but that's more just because we're so used to how they look on just the phone's screen.
