I've become an expert in low-budget veggie cooking; here are some suggestions:
Buy cans of beans, baking potatoes, olive oil, veggies of your choice, rice, pasta, tomato sauce, bread, peanut butter, jam, a vegan butter like spread, rice, almond or soy milk (for cereal or baking), lentils, hot cereal grains, mushrooms and any items you love.
Bake a potato for an hour+ in a 400F oven (wrapped in foil) then open it up and top with green onions, mushrooms, olive oil, pepper etc (or spiced canned beans or vegan canned chili)
sandwiches - toast bread and make an avocado tomato, lettuce sandwich, or other veggies, or make a pbJ.
soup - cook up a mirepoix (equal parts chopped onion, carrot and celery with a bit of olive oil (a few tablespoons) till slightly browned) then add veg broth, grains (rice, barley etc) (and/or lentils or beans) and any veggies you have around for a nice soup (simmer till the harder veggies are cooked through) (pepper, herbs and salt can enhance flavors)
cooked pasta and sauce is always a great choice
Stir-fry - Cut up veggies (onions, broccoli, carrots, mushrooms, potatoes etc) and saute them (a light fry with a little oil, just slowly add the harder veggies first followed by the softer ones in the heat till cooked), add a little soy sauce or bottled stir-fry sauce and serve over cooked rice (invest in a rice cooker... it is a necessity in any kitchen)
cook hot cereal on the stove or in your rice-cooker for an awesome breakfast (don't forget to add a little salt and pepper to taste and perhaps a little olive oil if desired)
roast - Cut up chunks of your favorite veggies and bake at 350-400F till cooked through (about 30 min to 1hr) with a bit of seasoning and olive oil for a nice veggie roast. (best if cooked covered to keep in moisture.)
Marinate some mushrooms (and/or other veggies) in your favorite sauce (for 20-30 min) then cook on a grill if you have one till soft. Serve by themselves or over a bed of rice or pasta.
Notes: ultimately I find that the key to cooking is practice and attention to cooked foods. Over time you will learn when items are done by their taste, color and texture. Just as pasta is known to be done by tasting the noodles as they cook, keep a fork or spoon by the stove and don't be afraid to poke at the food you are cooking to see if it's done yet. If it feels or tastes undone... cook it longer. but if the fork effortlessly sinks into a piece of potato, carrot or other veggie, it is likely ready to eat. As for seasoning; the key is to not over-season as salt and pepper, spices and herbs can always be added but not removed. invest in a Mrs. Dash or other similar seasoning blend instead of a bunch of different herbs and spices. If you are comfortable with adding a few teaspoons of spice to a dish before hand... go for it, otherwise, put a Mrs. Dash salt free spice addition (plus a salt shaker) to the dinner table and let those eating add it themselves.