the best way that i have found is this:
after your cham has eaten and you see it doing that licking thing with it's mouth, put a little drop on it's tongue, or if it's thirsty, hold a drop of water on the end, just squeeze the syringe slightly to hold a drop of water on the end, make sure your chameleon can see this, if it doesn't take it place the drop on the front of it's mouth. eventually it will drink it, if not keep trying.
syringes are not the best thing, the rubber seals tend to make control difficult if your using the same one over and over. best thing is a glass syringe or a pipette.
When your giving your chameleon water using a syringe or something similar, dont keep pileing the water into it's mouth, hold a drip on the end and let the chameleon take it, they will rear back after 1 or 2 drops to swallow, which is the signal to stop, i usually hold a drop on the end of the syringe and wait for mine to swallow, mine extends his tounge and i know he wants more.