How can I connect a Shure BETA 58A Vocal Microphone with a Samsung Galaxy S4?
You can use a cable like this to connect the microphone to the 3.5mm jack headphone slot in your smartphone. That one is said to be working with a Galaxy Camera, be sure to check on Google and on users' feedback for the compatibility.
Important: you have to search, in general, for a cable which switches from XLR (the connection present in your microphone) to mini jack or 3.5mm jack (the headphone slot in your phone). The XLR has to be female (holes for the pins), while the jack must be male (the jack pin coming out, to be inserted in a jack hole). Be sure to check five times in the internet for compatibility issues and extra steps needed to make it work.