Check out individual Tiny Thief level solutions here.
Always tap on all background details as they might be interactive, yielding up treasure.
Sometimes you'll have to tap on an object multiple times before you can get your hands on the goodies contained within. If you notice a small movement after interacting with something, keep tapping away to see if an essential item eventually appears.
Experiment with the different objects you find, and think about how they might be connected with one another.
Somewhere on each level is your furry little friend.
Keep in mind some breakable items need to be caught by our hero.
Since there's no time limit take your time and observing scene and enemy patrols before coming out of hiding.