Vegetables provide plenty of water, minerals, vitamins, and dietary fibers.
They are also anti-inflammatory.
They have extremely low energy level, very little calories, which means you can eat them as much as you want, with no limits, without risk of eating too much or getting fat.
You can put them in smoothies as well.
Some vegetables have more nutrients when cooked. For example Vitamin A from carrot is better absorbed after carrot is cooked.
Some other vegetables lose part of their nutrients during cooking.
Generally you can eat them both raw and cooked.
You can combine them with meat, fish and other salty foods, in every meal.
You can also add some healthy fats, like olive oil to make great vegetable salads.
If you eat non-organic vegetables, don’t eat too much, because they contain pesticides. Also WASH THEM THOROUGHLY, to wash away pesticides.

Potatoes are a special category, due to high starch content they are more similar to grains than to other vegetables. Potatoes are best cooked, frying them or roasting them with oil causes them to become too oily and too caloric. Potatoes provide a very good source of energy, just like grains. They can also be combined with legumes, meat, fish, other veggies etc. Eating too much potatoes can make you fat, so use some common sense, do not to overeat them.