Depends heavily on the depth to span ratio and stiffness of the cap. If the cap is basically rigid compared to the piles and there are lots of piles then my hand method is basically:
-Solve for the pile forces based on the applied column loads
-Then I treat the pile forces as an area load/gradient on the bottom of the cap and my columns as supports to come up with my maximum moments.
- Find max shear by inspection, as well as checking for punching
As soon as it gets into something that looks like deep beam theory I go strut and tie if it's critical, especially if it's only a couple of piles, and other more straight forward deep beam approximations if a bit more safety factor can be built in.
If there's fewer piles and a less rigid cap I might go with plate theory or FEA
There are lots of ways to solve this type of problem depending on the conditions, and all of them are a little bit fiddly.