Odds of Getting In
If you really want to be a stonemason, it isn't terribly hard to get in. The most important part of your early career is your apprenticeship, which is basically an internship without the tie. A master stonemason must be willing to take you in and oversee your work, so you'll have to prove to them you're both physically and mentally up to the task. Once they take you under their figurative wing, your apprenticeship will begin.
During these three or four years (yes, years) you'll learn all of the tricks and tools of the trade, from shaping and installing stones to basic geology and which materials best fit each situation. You'll know pretty quickly if this career is right for you, and if you don't, you can be sure your mentor will tell you.