As I said, a tandoor is a clay oven, it fact it is basically little more than a very large play pot, large enough to hold a good sized fire and then all the food that gets placed in it. Typically a tandoor is dug into the ground or built into an enclosure. The real secret is that heat can only escape it through to top. The direct heat of the fire is reflected by the ceramic sides intensifying the heat and creating a cooking environment that easily reaches 500 degrees F. It is buried or enclosed to hold in the heat and to keep anyone from coming in contact with the outside surface.
The marinade used in most any tandoori dish starts with yogurt. While this might sound a little strange this is actually perfect for marinating meats because it has a natural acidity and it is thick so it holds to the meat well and keeps the herbs and spices in place. The flavor of the yogurt (always plain) is so mild you typically don't even taste it. If you choose not to use yogurt in your marinade that's fine too, just make sure that you work the spices into the meat to get as much flavor as possible.
As for the spices, tandoori is marinated or rubbed with a great combination of spices. The first thing you will notice is the color. Tandoori dishes are usually very red or very yellow; this depends on the marinade ingredients. The red is provided by ground annatto seeds which can be somewhat difficult to find at your local store. The yellow comes from saffron which can be very expensive. Of course you can always go with the cheaper solution: turmeric.
In addition to the colors provided by the spices, tandoori is also flavored traditionally with ginger, garlic, coriander powder, cayenne pepper, and garam masala. Garam masala is a combination of roasted and ground cardamom, cumin, cinnamon, cloves, nutmeg and black pepper. This spice mixture is great on practically anything because it imparts a mellow but savory flavor to whatever you use it on. You adjust the heat of your tandoori dish by adding more or less cayenne pepper.
So, after you have combined your spices and yogurt, got the right color and heat, baste it over your meat. You want meats to sit in this thick marinade for several hours to absorb the flavors. Now you are ready to hit the grill. Remember that tandoori is cooked at very high temperatures and while you probably don't have a tandoor in the backyard your grill will do the job perfectly. Get your grill as hot as you can and keep it closed as much as possible. You want to start out at a high temperature and keep it that way. Lift the lid only long enough to get the meat on the grill and to keep a close enough eye out to prevent burning.