It's really easier than you think.
1. Before starting grill, spray grill rack with butter or oil (I like olive oil)
2. Lightly spray oil and spice the vegetables (Pepper, Salt, Garlic, or whatever spice you want)
3. Grill on low, closing the grill cover to help heat more thoroughly
One can "grill" veggies in the oven too. Same directions except don't spray oven with butter oil. Spray & spice veggies in pan and bake high or broil
Corn is a little different, for the husk is so thick. Better to wrap in foil or as Skippy mentioned
How does one grill vegetables? I'm pretty good with meat, but never tried something like corn or asparagus.