What's the best method for removing a oil dip stick that broke off in the well?

Remove the tube and stick assembly, push the stick out from the bottom, install the tube using a little sealant where it goes into the block then replace the dipstick with a new one! Dont know what eng. you got, didn't give that info. so it may have a bracket that needs the bolt removed from it. This will save you some time cause it is unlikely you will be able to fish it out! Either way, good luck.