We primarily used this extensive guide at Simply Recipes, with some tips from Bon Appetit and with consultations to the WaPo article, Julia Child, and my vintage Joy of Cooking from the 60s.

1 Goose (8-10 lbs, ours was 8.77)
salt, pepper, thyme and sage for rubbing
1 lemon
1 head of garlic, unpeeled, with the top cut off to expose cloves
1/2 medium onion, peeled and quartered
Optional: root vegetables, diced to a uniform size (~1") for cooking.  Potatoes, carrots, parsnips, turnips, celeriac...

For the gravy:
1/2 cup Madeira or red wine
2 cups chicken stock
1 tsp thyme
1 T + a bit of flour
1/2 onion, chopped

If the goose is frozen, defrost in the fridge for two days.  Bring to room temperature before cooking.

Remove the giblets and neck, and use a boning knife to remove the last two joints of the wings. cut across the side of the joint, severing the tendons. Bend the joint the opposite way it is supposed to go to break it. Cut the remaining skin and tendons. You should not need to cut bone.   Refer to http://www.simplyrecipes.com/recipes/how_to_roast_a_goose/ for visual guidance.  Reserve these parts for the gravy.

Remove the extra fat - start with the fat inside the body cavity. Remove the belly flaps covering the body cavity and the pope's nose (the tail). Slice off the neck skin 1/2 inch away from the body.  Place the fat pieces in a pot with just enough water to cover the bottom (about ½ cup) and put over low heat to render out.

Using a clean needle, make small, tangential pricks in skin all over breasts, sides, legs, and thighs of each goose to allow fat to be released during roasting (do not pierce flesh). Pull out remaining pin feathers with pliers.

Preheat the oven to 325 degrees F.

Rub the goose all over with the cut half of a lemon. Use both sides to get it good and coated. Put the halves inside the goose. Sprinkle salt, pepper, sage, and thyme  all over (and inside) the goose. Use more salt on the skin than you think you need; it helps crisp.

Slice off the top of a head of garlic and place it with some of the onions inside the goose.

Place, breast down, on large rack set in large roasting pan.

Put goose in oven, begin work on the gravy, below.

After 20 minutes, remove from oven and optionally add the root vegetables, tossing them in goose fat.  Remove as much of the fat from the roasting pan into the rendering fat as you can (leaving all the juices).  Return to oven for 25 minutes, or until the breast meat reaches 145F.

Carving the breasts off (pulled straight from http://www.simplyrecipes.com/recipes/how_to_roast_a_goose/, which also has great visual guidance here)

Using a boning knife, Carve around the legs and then slice upwards along the keel bone. Go straight down and tap the point of the blade against the breastbone as you move the knife up toward the wishbone, then back toward the open body cavity. A goose has a deep keel and that the breastbone comes out wide at almost a right angle from it, so work your knife in short, gentle strokes out to free the whole side of the breast. Once you get near the wishbone, find it with the tip of your knife and carefully slice around it and the shoulder. Repeat on the other side.

Remove the breasts and tent with foil, return the remainder of the goose to the oven, for approximately another 45 minutes, or until it reaches between 165-175F.  Remove, empty the cavity (using the garlic and onions for the gravy), and tent with foil.

Finishing/Searing

Now get a large sauté pan hot. Add some goose fat, and warm it up on medium-high heat.

Take the goose breasts, which should be a lovely pink (not purple - heat them up a bit more) on the meat side, and pat them dry. Place them skin side down in the pan and sear the skin. You might need to press down on them a little to get good contact. Check after 3-4 minutes, aiming at a rich brown.

Remove the breasts (don’t cook them on the meat side) and salt the skin. Set aside, skin side up. Move the pan off the heat.

Carve off the legs and wings of the goose. Get the pan hot again and sear the skin surfaces of the legs and wings. While this is searing, warm up the breasts in the oven, and then slice the breast (at an angle is nice) skin side up. Salt the legs and wings and serve with the root veggies.

For the Gravy:

Chop and brown all the giblets, wings and neck in some goose fat in a large pan. Sprinkle salt over them. Add the chopped onion and stir to combine. When the onion gets a little browned, sprinkle the flour in the pot and stir to combine. Cook this over medium heat, stirring often, until it smells nutty – about 5-10 minutes.

Turn the heat up to high and add the Madeira (sub in port or a light, sweet red - chianti, grenache, pinot noir). Let this boil furiously for a minute or two, then add the chicken stock and stir to combine. Add the dried thyme. Turn the gravy down to a bare simmer.

When you remove the bird from the oven,  Take the garlic cloves from their husk and put them into the simmering goose gravy. Let this cook for 5 minutes. Fish out the neck and wing pieces and pick off any bits and toss them into the gravy. Blend the gravy (in batches, or using an immersion blender). You want a thick gravy, so if it is too thick add water. If it’s too thin, don’t worry, you can cook it down.  Return the gravy to the pot and put on low heat. Simmer it more if it is too thin.