>I am struggling to think of ways to cook veggies.

Something very easy that I do sometimes is this:

1) preheat your broiler
2) take whatever veggies you have in the fridge and cut them up into
smallish chunks.  I like to mince a shallot in with them
3) toss them in some olive oil, then spread out in a single layer on a
cookie sheet
4) season them to your taste (I usually use salt, pepper, and rosemary, but
you can use whatever you like)
5) stick them under the broiler for 10-20 min, or until they start going
brown on top
6) smack your lips and eat!

You can also try just sauteeing various veggies using different spices to
totally change the nature of the dish.  For example, using Indian spices
will make a dish of carrots and broccoli vastly different from using, say,
thyme or oregano.

Another thing I just thought of (after watching Good Eats with Alton Brown)
is a veggie soup.  Just simmer whatever veggies you've got in some sort of
broth, add seasonings, maybe a little fresh parsley for color, and you've
got a nice veggie dish to go with dinner.

-Elizabeth