Some chameleons accept water from an eyedropper. Especially, if trained from a young age. Your chameleon may not "get it" for a while, but keep trying, they do learn! Hold the dropper about 5 inches away from your chameleon's face, so it can see the droplets. You may let several drops fall gently on his "lip".
The only catch to this method is that someone has to be there to administer the water. Therefore, it's only a method that works as long as you are around to offer your pet a drink. You can purchase RUBBER (never glass, as they can bite them and injure there mouths) eyedroppers at your local pet or drug store.
Fill a small cup up with water and show the chameleon the water in the dropper, slowly dripping out. Your chameleon will be attracted to the droplets of water glistening in the light. Let a few drops fall on its nose if it does not respond. It may take a few times before your chameleon learns what you are trying to do!
Another trick is to mist them lightly, so they start to open their mouths, licking the moisture in the air and then start to drop water in their mouths slowly! You do not want to force water in. Remember they drink by lapping with their tongues and do not gulp water! As soon as they know its water, they will continue to move towards the dropper. If you see your chameleon tilting his head, nose to the ceiling, he is trying to drain the water he was collected in his gullet so give him a chance to do so before giving him more.
Some people place ice cubes on the top of the enclosure, and allow their chameleon to drink while it melts, however, it does not provide a constant source of water. You can also place ice cubes in a large plastic cup with a small hole in the bottom, creating a slow drip. You must also provide a catch basin for the water dripping down into the enclosure.
The only catch with this method is that you MUST ensure there are branches near enough to the water droplets so your chameleon can reach them. You will also want to ensure they can't get to close to the basking light! Make certain you use a container with significant weight to it, or your chameleon can knock it over and cause a mess. I also place a few large rocks in the container, to ensure a smaller chameleon cannot fall in and drowned!
Chameleons are attracted to droplets of water suspended from leaves glistening in the sun. When you sprits the walls and foliage in your chameleon's enclosure, ensure there is enough to form drops for your pet to lap up. Misting the mesh screen lips of the enclosure is a good idea, as droplets easily form and suspend for a good period of time before dropping. Make sure your chameleon has access to the water, like a branch that reaches the top on the cool end of the enclosure.
Even if your chameleon does readily drink, allow it to follow its instincts and sprits the leaves heavily, so it has the opportunity to lick the water droplets off of them.
You can then either purchase a "reptile hammock" with a pond in it that hangs in the corner of your aquarium or just fill up a shallow bowl with water. You can purchase an air pump for about $9 at any aquarium store. The air pump creates bubbles that seem to attract most chameleons.
DO NOT use this method for babies, as there is a significant risk of drowning. ALWAYS place rocks in the bowl or glue a thin stick across the blow to aid your chameleon if it accidentally falls in.
The water must be changed daily and the bowl sterilized at least once a week. Remember, chameleons tend to go to the bathroom in water, and insects fall in and die, so if you are using this method you must ensure that the water is clean at all times!