This page began as a Usenet article that I posted to alt.food.vegan.
I don't have a precise recipe, but this is one of those things where a precise recipe isn't what you want, anyway — the amount of oil and cooking time will depend on what vegetables you use, and how much of each, and what you cook them in. There are lots of variables there, but no need to be scared; if you keep an eye on the veg as they cook then you'll do fine. It's not like cakes or something where you have to be careful not to open the oven too much or it'll all go wrong.
Vegetables that will probably behave well for a beginner include: carrots, aubergines (eggplant), courgettes (zucchini), button mushrooms, potatoes, peppers, parsnips, squash, tomatoes, brussels sprouts.
Cut up veg into chunks. The chunks will get smaller during cooking, especially with the more watery vegetables such as courgettes or mushrooms, so bear this in mind when you decide what size to make them. Also, some vegetables cook quicker than others (think courgettes compared with potatoes) so you can help them be done at the same time by cutting the quickly-cooking ones in larger pieces than the slowly-cooking ones. (If you want the pieces all the same size, that's fine too; see the paragraph below about staggering the cooking times.)
You can put all the veg in the oven at the same time, or you can put the more slowly-cooking ones in first and add the others after they've had 20 minutes or so. It's up to you. Experiment! It's unlikely to turn out horrid. Even over-mushy vegetables aren't so bad when they've been roasted to a nice, dark, sweet, caramelised state. So, if you're not putting them all in at once, make sure to keep the later ones separate at this point.
Mix the veg with olive oil and optional seasonings. The amount of olive oil is up to you. You can even leave it out entirely if you want no added fat, but then the veg will be more likely to stick to the cooking pan. You don't want the veg swimming in oil; just add enough to give them a nice sheen. Mix it in well. Seasonings that are nice include celery salt, black pepper, paprika, chilli powder, lemon juice, tomato puree, garlic puree, soy sauce, balsamic vinegar, dried basil or oregano, and so on.
Now the choice of cooking pan.
Using an oven dish with high sides will reduce the evaporation of water from the vegetable mix, particularly if you fill it more than about half full. This kind of dish will make the vegetables end up more juicy, but you run the risk of them being soggy, too. This might be what you want, though, for example if you were going to mix them into a pasta sauce. You'll probably want to be sure to stir the veg a few times during cooking with this kind of dish, so you don't have the same ones sitting on top all the time and cooking differently from the rest.
Using a baking tray will allow much more evaporation, particularly if you use few enough vegetables that you can spread them on it in a single layer. This will result in the vegetables being less juicy, but more “roasted” tasting, with the outsides becoming well-caramelised before the insides are overcooked.
As for how long and what temperature to cook them — experiment. I've cooked roasted vegetables at all kinds of temperatures depending on what else I was using the oven for at the time. Check and stir them often to begin with, until you start to learn how all the different variables work together. They're done when they taste good. Be sure to test more than one type of vegetable for done-ness, until you've got the hang of it and can judge it by eye and/or prodding.