If this is homework? It very possibly is, because there are relatively few good reasons I can think of to solve any integration problem over a sphere using Monte Carlo. So if it is homework, then you need to do your own homework. At least make some effort.
Regardless, even if this is homework, it is still trivial. Just generate points uniformly distributed over the sphere. Then add up function values at those points. (Be careful to scale by the volume of the sphere.) WTP? I can think of several ways to generate uniformly distributed random points inside a sphere. You should even be able to use a weighted Riemann sum, if your generation scheme was not uniform.
The problem is, Monte Carlo is not very efficient as a method. You will gain far more accuracy in your result by using any of a variety of schemes for integration over a simple domain.
The only circumstance when I could see using Monte Carlo on a spherical domain is if your function is itself strongly discontinuous over the domain of the sphere, with many discontinuities, derivative singularities, etc.
So in any case, you need to convince me this is not homework. And then you need to convince me why it is that you think you really need to use Monte Carlo. I won't spend the time telling you how to solve a problem poorly.