They generally will eat on their own. If it moves, they'll eat it.
I have a plastic tray in all my cages, although two of my chams can and will eat from my hand. The one that doesn't, tends to eat from his tray when I'm not looking.
From a very early age when they are mostly eating crickets, I put all the crickets in a small feeder cup. They see a few of the crickets jump out and go for them and then come back to the cup for more. If you buy from a pet store or a big breeder they probably have never cup feed the babies and I don't recommend it when you first get your chameleon. Free range his crickets for the first few weeks. He/she has enough to get use to with a new home and all new people so he's already scared and I wouldn't make him have to do yet another different thing just to get his food.
I have only had my Veiled for a week and I have yet to see her eat, I assume its because she's still stressed from the new home plus 3 days after I got her she went into shed, I have tried to hand feed her and she wont take it.
The placement of the cup is also important - place it under a vine or branch that he frequently sits on or walks along. The cup should be opaque or they will try and shoot from the side or even underneath and may damage their tongues. They need to be able to look down into the cup.