You can freeze your vegetables in just about anything, but the easiest are plastic freezer bags (like Ziploc). You can also freeze in canning jars, plastic containers, aluminum foil, plastic wrap, and freezer paper. Just make sure to leave room for the veggies to expand as they freeze.
Before you put your vegetables in the freezer, you will need to blanch them, which means you will heat them in boiling water for 2 to 3 minutes and then immediately cool them in cold water. This kills the enzymes that age vegetables and will help them to taste better when thawed. The quick submersion in cold water stops them from cooking any more.
To prevent darkening in some vegetables, you will need to soak them in an anti-darkening agent like lemon juice before freezing them. Use one teaspoon per quart of water and soak for about 5-10 minutes. There are also commercial preparations for soaking available.