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Amanda is a co-founder of Food52.
Make sure you toss them in oil and spread them out on a roasting pan or baking sheet. There should be space between each vegetable so that it's touching the roasting pan and will brown. If the vegetables are piled on top of each other, they'll steam rather than caramelize. Also you want to roast the vegetables at 375 degrees or higher. Good luck!
Use a hot, preheated oven (425-450 F). Preheat the sheet pan as well, if you think of it.
Don't be stingy with the oil (it helps conduct heat, which promotes browning).
When first placing the vegetables on the pan, don't crowd them (crowding inhibits browning).
Once they're in the oven, just let them be for 10 minutes or so. Don't be stirring them around every 2 minutes.
Salt the vegetables just before you put them in the oven (my preference) or just after. If you salt too early, it pulls out water, which inhibits browning.