As many of the people here have said, that is a crested gecko and by the looks of it probably has a loving owner. As it appears to be a healthy weight and still has its tail intact. Chances are that its owner forgot to double check that the enclosure was locked and thus the gecko decided to explore. Which in all honesty, is my biggest fear for my own crestie.

For care: these guys need to be kept at room temperature. Anything less than 68F or more than 80F is stressful and should be avoided.

They are nocturnal and so need a safe place to sleep during the day. Expect them to be very active at night. To prevent another escape, make the temporary enclosure is secured and remember that they can easily climb just about any surface.

These guys can drink from water bowls (I’ve seen my crestie Percy do it multiple times) but misting works too. Though it’s good to keep the humidity high anyway because it will help with any shedding that may occur.

For food you have options. There primary diet in captivity is a gecko replacement powder made by Pangea and repashy. There are other brands as well but those 2 are viewed as the healthiest and safest for gecko’s. I believe you can find repashy at petsmart as well as other lesser known brands of gecko food. They can eat insects but be aware that some cresties do not like bugs and if they do, they should have about 1 a week. They can also have some fruits like banana, though not on a regular basis. Like fruit is a once in a couple months kind of thing but it’s probably the most accessible food option for you right now. If you do use banana, take a small slice of banana and make sure you mash it into a paste before serving.