How do I adapt to grilling without a lid?

While if you have the opportunity to improvise a lid I recommend you do so as per the other answers, however it isn't always possible. I have unexpectedly been thrust into the "grill master" role when I've shown up to parties and the charcoal is hot, food expensive, and nobody but me knows how. In situations like this you have to do the best you can with what you have, and sometimes you won't have a lid or anything you can use as one.

The reasons you want a lid are that it evens the heat out, and reduces the oxygen supply to the fire which cools things down a bit and reduces flare-ups. Without a lid you will get a hotter temperature at the base of the grill and much cooler temperatures above, with fat having a much greater tendency to flare. You can still get good results through making good choices of what to cook, and good technique. Bad technique will lead to food that is burnt to a crisp on the outside and raw in the middle.

There are some foods that you don't need a lid for, in fact you shouldn't use one, like thin to medium cut steaks. Other foods like burgers you can use a lid or not and still get a good result. So part of your success will come from choosing the right things to cook. Thinner is better, as is picking foods that don't necessarily have to be cooked through.

Some food you just can't grill without a lid. Avoid anything that requires long, indirect heat like legs of lamb or roasting joints.

Some food is best cooked with a lid, but you can get good results without one, like chicken and sausages. Your main problem is heat control, and flaring. Chicken and sausages need longer cooking temperatures, so the goal is to cook them through without burning the outside, you can do this by keeping them around the edge of the charcoal where they get enough heat, and dripping fat won't hit the coals and flare up. Turn them often, like once a minute to keep them from burning. If they are getting close to done and they don't have enough char then you can move them to the center of the grill for a bit. It also helps to have some sort of baste to coat them with to keep them moist like bbq sauce or a marinade. With sausages you can cheat a bit by slicing them down the long way and cooking them flat a few minutes over high heat.

If you are cooking different foods at the same time, like burgers, sausages, and chicken then separate your grill into zones. Burgers get high heat, sausages medium, and chicken low. If you want to cook mostly food that needs a medium to low heat then you will get a lot of mileage from arranging your charcoal intelligently, like in a long strip down the middle of the wide part of the grill, or in a square grill in a torus shape. This will give you much more area of your grill with the temperature you need.

Really important for lidless grilling is a spray bottle full of water to put out flare-ups, a mist sprayed on the base of the flare works magic and it won't kick up ash all over your food.