Preheat oven to 400ºF and place the rack in the lower part of the oven.
Cut (and peel if needed) vegetables into bite sized pieces that are similar in size. If pairing vegetables together, make sure to choose ones that cook in the same amount of time. See the body of the post for pairing vegetables.
Arrange vegetables on a baking sheet and add oil, salt and pepper. Mix together with your hands then evenly spread out the vegetables, making sure to leave room in between.
Roast soft vegetables such as peppers and green beans for 20-25 minutes, flipping half way through and hard vegetables such as potatoes and root vegetables for 40-50 minutes, flipping half way through.
The body of this post has a lot of information about roasting vegetables, including tips and suggestions on pairing vegetables together.