I give the equivalent of 1cm cubed sized (doesn't actually have to be square!) - ie a cube of cucumber or carrot - a floret of broccoli about the same size. They can have that daily. It's about right for a syrian and about the same as thumbnail sized
Just one piece a day. But varying what you give them is good so it's not the same veg every day. Or a single pea. A syrian will eat all of that and not hoard it (so it doesn't go off). On the rare occasions ours haven't eaten all of it, they leave the rest where you put it (ie put it on a separate little dish to the main hamster mix on the other side of the cage so they have to get some exercise to get it!). The rare occasions are usually something they don't like. The only dislike I've had from some hamsters is raw carrot! They seem to prefer the green veg - cucumber and broccoli although they do seem to like cooked carrot - but raw is better for their teeth.