Not too difficult, most recipe books have it.
Pre-heat oven to 350f
Trim the rack to your liking. Some like all the fat on, some 100% trimmed. In your photo, I think that most of the fat has been trimmed.
Season the rack – salt& pepper all around. If completely trimmed out massage with oil first, I use EVOO.
In a HOT heavy pan, cast iron works best for me, sear the lamb. You want the color to be a deep mahogany, none of the wimpy light brown.
Put rack in pan in the oven, ribs up, for approximately 15 min.
Internal temp should be 120-125 for medium rare.
Take out & put on a wooden board & cover with foil, rest for 10 min. VERY IMPORTANT.
Deglaze the pan w/red wine & demi-glace, mount the butter & serve