Oh man I'm jealous!! Fresh tuna is one of my all time favorites.
I'd probably cut it at least in half lengthwise. A lot of times they will kinda just cut across the fish, so the hunk you end up with will contain both loin and belly. If this is the case, it's a good idea to separate the two parts as there is a blood line running between the two that doesn't taste very good. It's easy to spot. It'll be much darker than the rest. Just carve that part away.
Anyway, like I said I'd cut it into fairly large rectangles. Steaks are good, but really easy to overcook. I'd probably smoke at a low temp, say 200° just to get some smoke on it. I wouldn't want the internal temp to get over 110°. Then I'd sear it in a hot skillet or over very hot coals to an internal temp of 130°. Tuna is really best at medium rare. It doesn't need a brine or really any seasoning other than salt and pepper. The most I'd do is a short marinade in Italian dressing.
Once it's cooked, slice thin and enjoy!