Getting them to drink on their own is tricky. IMO captive iguanas don't naturally drink from standing water. It's not because they're not thirsty, it's because they don't recognize it as water.
Visitors to Costa Rica have reported seeing iguanas emerge from the treetops to eat flowers and drink the rainwater flowing on tree branches during rain showers. They see this from their hotel's second and third stories. They are reported to suck on running water that flows down the trunks of trees. I'm sure the wild iguanas do learn to drink from standing pools, or they wouldn't survive the dry seasons. I once saw one of my favorite iguanas sucking hard on a large wet rock.
So I took all that in, and finally started training them to drink from water that flows into the tub during tubbing. My rescues never liked the sights and sounds of the bathtub, including the soft squeal of the tub's faucet when it was opened a bit to let water dribble in. But some did learn to dink when put into the tub. I submerged their heads as they slid in. Their drinking is subtle, and happened when they moved their chins close over the water, as if they were looking around, just after they were put in. When I was alerted to this, I listened, and could usually hear slight slurping sounds. My pet iguanas had the most experience, and they drank the most.
I finally settled on a way to teach my rescues about standing water. I would make several 6 inch wide shallow water containers (the bottom 1 inch of cottage cheese and yoghurt containers) scattered across the floor of the enclosure, to make sure they would walk through them at times during the day/night. It seemed to work. These iguanas usually soon (after a month or two) learned how to drink from containers and the tub. I used that method for years, although I never was convinced they drank enough.
A good solution is to use a pet store waterfall feature inside the enclosure. I had to cover them with 3/4 inch mesh screen to keep the iguanas from pooping in them. I'm convinced that would work, but the problem was, the waterfalls became overgrown with algae, requiring bi-weekly cleaning, which I guess I was not willing to do.
Hope some of this helps.