I used to live a couple houses down from a Turkish couple, and this is how they did theirs back in the motherland:
In a blender, dump in 2 pints of Greek yogurt, a cubed up red onion, 4 garlic cloves, a handful of parsley, squeeze the juice of 2 lemons, and salt the hell out of it. Crack in plenty of black pepper. The mix will need to taste too salty by itself, but with the addition of meat, will even out. The salinity should taste as salty as (or a little less salty than) seawater. Run blender until it's all smooth. Cut the thickness of the yogurt with some good green extra-virgin olive oil. The mix should be fluid, but not runny.
Cube your meat (marbled beef ribeye, lamb, or other game), and mix it with the yogurt stuff above for at least a day in a Ziploc bag.
After a day, take the meat out, and pat it dry. Don't rinse the yogurt off with water, but get the majority of it off with paper towels. Skewer the meat onto metal skewers, and skewer the veggies onto separate skewers.
Grill over very high heat (wood coal fires are best), and baste with the yogurt.
Garnish with ground sumac, and serve with a tzaziki sauce.