Okay, first off there isn't a 'guaranteed' chance of getting a mutation, just because one is *possible*. Patience is a virtue you will need, should you wish to breed bees.
First, you establish a pure Noble strain. If you are playing with Extra Bees, you will want some Noble drones, because Noble crosses back with certain other lines.
I'm also going to assume you have a stable Cultivated line that you wish to maintain.
Now then, Soul Frames are your friend. They increase the chance of mutation. Three soul frames in the apiary that you cross your PURE Noble princess with your PURE Cultivated drone.
If you see any Drones with 'royal', use them. But if all you get are Noble/Cultivated hybrids, then remove the soul frames, and breed Noble drones back in to get a pure Noble princess. You might luck out with Majestic, in which case go back to using that, but you primarily want to try and use pure-bred rather than hybrid bees for your mutations.
Once you get Majestic, things get complicated. Majestic isn't all that useful, you want Imperial. Fortunately, it's surprisingly difficult to establish a Royal strain. So if you get, say, Noble/Majestic on your Princes, and cross with a Magestic/Noble drone, you can end up with an Imperial because Magestic + Noble = Imperial.
So, when actively trying for a mutation, use Soul Frames (Impregnated Frame + Soulsand), when trying to purify the strain, pull them out.
EDIT: Thanks for catching that, plznt3r