Yes dolphins do sleep.
Even though it may seem like the dolphins do not sleep they actually do sleep.
Dolphins usually sleep while slowly swimming or even while just resting in the water.
The dolphins do have 2 basic ways of sleeping in the water and those 2 ways of sleeping for the dolphin is to either sleep while swimming next to other animals in the water or they will sleep by quietly resting in the water, vertically or horizontally.
If you go to an aquarium or somewhere else where there are dolphins you can observe them sleeping and that's how the dolphins will sleep.
This is how researchers and observers have discovered how the dolphins would sleep.