You'll need a Dutch oven, or something like it. I used a Le Creuset pot.
--A whole chicken
--Salt and pepper, garlic, thyme
--A lemon
--Some dry white wine
--Oil
--Vegetables: I used potatoes, onion and mushrooms, but celery and carrots, maybe a turnip, would have been excellent, I just didn't have any.
Put a tablespoon of oil into the pot and get it hot. Coat the chicken in a mixture of salt, pepper, thyme and garlic powder. Stuff a lemon into the cavity.
Plop the chicken, breast side down, into the pot for about five minutes to brown the skin. Chop your vegetables while it's browning. Turn the chicken and add the vegetables around it.
This is just after I've turned the chicken and just before I've added the vegetables. If you don't do this, the chicken comes out looking very peaked and sickly.
We're now at the point where cooks differ on how to proceed. To add liquid or not? In point of fact the chicken doesn't need any additional liquid. You can cover it and walk away. It won't burn. Me, I add some white wine. You can choose. You'll see later why I add white wine.
Cover the chicken and go do something else -- evidently, as proven for the umpteenth time tonight, anything other than football will do -- for half an hour. Check the chicken at the 35 minute mark. Maybe it's ready; check the temperature. If not, give it ten more minutes or so. When it's ready let it stand for a few minutes (chicken isn't like beef that has to 'rest' but it's still good to let it stand for five minutes). Then carve and serve with the vegetables and sauce.
The sauce surrounding the vegetables is the result of adding a glass of white wine. That's why I do it.
Once it's ready serve with a simple salad and bread. It's not precisely Poule au Pot like in France. But it works. And it's très simple. Serve with either the white wine you added to the pot -- I used a white wine from Saumur (In the Loire Valley and the home of the French Cavalry school), but a Pinot Noir from Bourgogne would do very well also.