I haven't dug anything that significant yet. Largest items were a piece of pipe, about 1/2 to 3/4" dia. and about 4" long. A garden nozzle and the cleanout cover for a drain pipe.
Maybe the diecast cars and some soda and beer cans would be similar in sizes but they were in sand where I didn't need to use much care digging them up.
Anyway, I would try to be as minimally invasive or damaging as possible. Especially when digging in the lawn or areas where there might be concerns for vegitation. Some forest situations might apply here. . If I were digging a street project, construction site, or other area where I didn't need to consider my damage, I might use a shovel, in the end, but would use these same procedures to start with. I would first, dig down till I hit the object. Probably using my hand digger (Lesche Predator). Digging carefully so that I don't damage what I am digging. I start by trying to keep the hole as small as possible. I usually have to dig several inches accross to be able to get my hand down there. I will start by widening the bottom of the hole, so that it is, sort of, bell shaped. Then, as necessary, I widen the hole. In the cases of areas where you don't need to be careful, it would still be good to dig, at first, by hand. Then expose the object you are looking for. Then, if necessary, widen your hole with a shovel to get around your object.
I dig over the top of the item to expose it and try and find the sides and or end of the object. I will, usually, keep digging around the outsides (edges) of the object, occasionally taking my lesche digger and catching under the target to pry upward. Once the object is exposed, I catch my digger, or you could use your shovel if not being delecate, and then try and use a little leverage till it comes free. Another tool that might be handy here, as I think about it, would be a long and very strong or stiff piece of wire or a rod with a hook on the end. Something that you might hook under an object and gently pull upward. A screwdriver might be good for working the edges some to loosen or free an item from the Earth's grip.
In the end, I try to have as small a hole as is humanly possible. I would add that the same basic practices would be good as when you dig a plug for a coin or something. Dig a flap with a significant enough dirt layer under the grass. Fold it asside and dig under it. Put something down and put your dirt in or in it. I was thinking the other day, some of those, reusable/disposable, plastic Gladware casserole dishes would be good. Large enough in size for a small hole and not metalic. So, unlike an aluminum pan or cookie sheet, they shouldn't effect your ability to search the dirt you pull out. Of course an old towel, sheet of plastic would be good to keep your area clean. Save the grass plug that came from on top. Maybe a small hand rake would be good to make sure you get all the dirt back into the hole. Refill the hole, replace the sod.... Water in and sprinkle with some cayanne pepper or something to deter animals from redigging the area.