How do people digest fat after gall bladder removal surgery?
This is not a problem, since the gall bladder "only" stores bile, but the production itself happens in the liver. There are some cases described which can get problems digesting very fatty food, but for most people this is not a problem. Additionally eating low-fat food in the first few weeks after the removal is recommended. See here for some more details.

The picture below shows the location of the gall bladder and also the bile ducts (picture from here)