When distilled down to its base values, Doodle God is a large logic puzzle based on matching. You're given four elements (earth, air, water, fire) at the start of the game and can combine them to make things. Combining fire and air gets you steam, fire with water alcohol (firewater, har har), and many others.
From there, you can use the products of your matching to make other things, which is where the game gets most of its depth. There are over 200 different elements to find, and more being added all the time. This is the major selling point of the game, touting the ability to make fantastical creatures, like the front end of an airplane and the back end of a horse.