At this point, I start my charcoal. I used a chimney starter full of Kingsford Charcoal and started soaking my Mesquite wood chunks (about 20 minutes, while the charcoal was getting ready). I built the fire in the smoke chamber of my smoker/grill because I was grilling relatively quick this this time.
When the coals are grey and ready I place my Mesquite wood on the coals and put the steaks on a grill that was about a foot away from the flames, and closed the lid. Don't be tempted to sear the meat upfront.
Go ahead and cook with indirect heat and smoke for 15 minutes on the first side. You may want to adjust your times based on various conditions. For instance, you will want to use the above time if the steak is at about room temperature to begin with, and outside temps are spring-like. If the steak has been thawed out and is still a little cold or frozen in spots, just go an extra five minutes on the first side. Likewise, if it is a hot summer day, you might want to cut the time back a little. Turn the steak over and let it go another 10 minutes on the second side.
Check the temperature often. For medium rare steak, cook to internal temp of 140-145. For medium steak (slightly pink) cook to 150, but not over. About 155 is the highest you will ever want to go, and that satisfies most well done steak lovers. If someone wants their steak a little more done, throw it over the coals and sear it uncovered for about 3-4 minutes on each side. That should get you 160, and hopefully prevent your meat from drying out. I cooked the steak in the (blurry) picture below to about 148 degrees at resting temperature. It is pink, but not raw.