It's a bit hard to answer very specifically because so much depends on your individual setup, your cham species and age, the temps and humidity you are trying to maintain in your location. I think most of us use a combination of drippers and hand or auto misting to regulate cage moisture. You want two basic things...to provide moving water for the cham to drink directly, and to raise the cage air humidity. Personally, I never got along all that well with drippers starting years ago with medical supply IV setups to the drippers sold by herp stores. I just never got the drip rate or duration I wanted. They either dripped too fast and emptied the jug before the cham decided it wanted to get a drink, or they dripped too slow and never captured the cham's attention or clogged completely. If your cham happens to be thirsty it may notice the dripping and take action sooner than one that isn't. The dripper may not last long enough for a thorough drink if your cham doesn't happen to learn that's where to go for water. Not all chams take to a dripper so don't assume yours will.
Once you start the dripper let it run until the jug is empty. The drip rate you'll have to experiment with yourself as every setup and every dripper is going to behave a little differently. No dripper is going to create so much splashing that it drowns the cage as long as you have the right sized catch pan below. If your dripper jug is a quart size you'll need a quart size catch pan below.
You want to arrange the dripper tube so the droplets splash the surface of a leaf or clump of leaves and even get partially held there, partially pool on the top, or at least create motion to attract the cham's attention. It seems simpler to just aim the drip into a plant pot, but you can end up rotting and killing the plant. Don't bother trying.
Many chams tend to start drinking if you mist the cage first, then set the dripper going once they have the idea that its time for a drink (like during or right after rain in the wild...I think of it as priming the pump).
A dripper alone in a screen cage won't usually be enough moisture to maintain cage humidity on its own. There isn't enough water volume evaporating all over the cage surfaces.
My own watering preference is still hand misting (or auto misting depending on where I live, work schedule, and the climate) with some extra ultrasonic fogging as necessary during drier seasons.