When you put a steamer in a pot of boiling water and put vegetables inside the steamer, how do you get them out after they are done? What tool do you use?
Tongs or large fork should work.
I imagine you are asking about steamer baskets like this:
I think most people just reach in with an oven mitt or pot holder, and lift it out with our hand. This particular image has a ring, but some have a knob to make gripping easier.
You can also lift out the food items themselves with tongs, and then wait until the steamer assembly cools and simply take it out with your hands.
If you are talking about oriental style steamers, traditionally used with a wok:
Again, just a tea towel or oven mitt is needed. The bamboo ones don't tend to hold as much heat, but I would certainly not pick up the metal variant with a bare hand right after steaming.
A draining spoon like one of these.
If you have a big colander, you can just put it over the top of the pot and turn it over, dumping the vegetables and the steamer in. The steamer is a lot easier to grab when it's not inside a pot full of steam, and you get it all done at once, no fishing around for the last couple pieces.
Chopstick through the ring in the middle. Or chopsticks to fish out all the vegetables.
A so-called "spider", like this: