The Meaning of Life, the Universe, and Everything.
Best thing I can tell you is to keep your dirt blocks away from grass blocks. Or Mycelium. Both will take over any dirt blocks you have and transform it into one of them. Kinda like what happens when you're bitten by certain zombies (not Minecraft zombies, who are shown not to bite)...
You could use a shovel to make a path instead of using regular dirt blocks (just tap on the grass block you want to convert to a path).
Brown and yellow stained clay? Other than using a different block, the only ways to stop grass growing on regular dirt are 1) keeping it separate from grass blocks so the grass can't spread to it (boundary can be anything, including planted farmland). 2) keeping the area completely dark since grass won't spread without sufficient light.
If opting to use option 1 - separating the dirt from the grass, keep in mind that the boundary has to be sufficiently wide and deep so as to keep the dirt out of the range of any grass blocks that can spread (3 x 3 x 5 per the Wiki - not sure if this is the same on PE).
Also, a quick way to kill off large areas of grass is to pour water over it and leave the water there long enough so the grass eventually dies.