Hi Klon99, welcome to the board! With small items that cook quickly (like steak) you would usually get a nice hot fire going- say in the neighborhood of 600 degrees or more. You would then clean your grill grate, and put a little bit of olive oil on the grates by dipping a paper towel in the oil and spreading it over the grates using a set of tongs. Cover your grill and let it come up to temp for 10 minutes or so, so that the grates are good and hot. I would then remove the lid (or lift it up) and grill directly over the coals or burners six minutes or so per side (for a one inch steak to come out medium over a HOT fire) rotating the steak 60- 90 degrees after 3 minutes to get a nice cross-hatch grill mark going, and repeat the procedure on the other side. This is the way that I would do most steaks (and grilled items) that would be done in 20 minutes or less. Dave, (I don't know if you miss-typed) you have the fundamentals down about why you would close the lid, but I don't know if you meant to close the lid if the item is MORE than an inch in thickness as would be the case. Although I find that up to an inch and a half steak can be grilled without the cover in my opinion. I did recently get some monster porterhouses that were in the area of 2 inches thick, and while the fire was quite hot, and I increased the time to 8 minutes per side, the steaks were not cooked through (to my wife's liking), Closing the lid in that case would have helped the situation. The general rule is there are no rules- have fun. However if the item is small and cooks fast a lid is not generally required. Larger items that take longer to grill, would be done using indirect heat with the lid closed (and at a lower temp).
As for the thermometer, try this link to get some ideas:
I have the Temperature detective which I am quite fond of, although there are similar products on the market i.e. Polder thermometers that do basically the same thing for less money, and should be easy to find in your local Home Depot, Kmart, Lowes etc. These types of thermometers are designed to be put inside the meat to test the internal temp, but if you are not cooking at too high a temp (<400- anything higher will damage the unit) you could leave the probe on the grates to get an accurate measurement of the temp that your food is being cooked. You might also mount a thermometer permanently to you grill by drilling a hole in the lid (and applying a little high heat grill paint to the bare metal). If you do, make sure that you mount the thermometer close to where the food is being cooked- because temps will vary quite a bit depending on where the thermometer is placed, you want to know the temp at food level.