Vegetables steam quickly and efficiently in the microwave, but each vegetable takes a different amount of time to cook. Depending on the size of the pieces and how dense the vegetable is, the cooking times vary from 2 minutes for less dense vegetables, such as kale; all the way up to 13 minutes for whole acorn squash. That said, some constants remain -- all vegetables need a bit of liquid added and need frequent checking as they near done-ness to help ensure that they don't end up overcooked.
Fresh Vegetables
Thoroughly wash vegetables just before cooking. Use a scrubbing brush for vegetables that might have ground-in dirt, such as potatoes or cucumbers with spines.
Cut vegetables into serving-size pieces with a chef's knife meant for chopping, or leave them whole. Whether or not you cut the vegetables depends on how you plan to use them. For example, leave beets whole if you plan to use some the same day and save some for another day.
Place the vegetables in a microwave-safe container and add water. Sprinkle a few drops of water on vegetables that already contain lots of water, such as broccoli or zucchini; and add up to 1/4 cup of water for longer-cooking vegetables, such as winter squash or beets.
Cook the vegetables until they are crisp-tender, meaning that they are no longer raw but have a little "give" when you poke them with a toothpick or the tip of a sharp knife. Check the vegetables in 30-second intervals as they reach their typical cooking time.
Frozen Vegetables
Remove the packaging from frozen vegetables and place the vegetables on a microwave-safe plate or bowl. You can microwave some vegetables in their packaging, as long as the wrapping is made from paper, not foil. Put packaged vegetables, such as spinach or green beans, in a bowl, since liquid from the ice will melt and drain from the box.
Cook frozen vegetables from 3 to 5 minutes, checking frequently for done-ness. Some vegetables, such as frozen corn, will cook faster than fresh varieties since freezing has already broken down their cell walls to some extent; but others, such as spinach, will take longer than fresh since they're frozen in a solid block of ice.
Drain excess water from the cooked vegetables by tipping the cooking container into your sink and holding back the vegetables with the side of a chef's knife. Use a potholder to hold the plate or bowl and proceed slowly to protect yourself from very hot steam and water.