For Borel set $A$ the Martin Capacity is defined as:
$\mathrm{Cap}_{M}(A)=[\inf\{\int \int \frac{G(x,y)}{G(0,y)}d\mu(x)d\mu(y):\mu \mbox{ probability measure on }A \}]^{-1}$ and Green's function $G(x,y)=\int_{0}^{\infty}\frac{1}{(2\pi t)^{d/2}}e^{\frac{-|x-y|^{2}}{2t}}dt$.
I didn't find any references online. All I found was http://www.math.upenn.edu/~pemantle/papers/martin.pdf. But they don't compute any Martin capacities there.
Ideally a step to step process.
Or at least a way to get estimates ,say, for compact sets.
Thank you
Have you consulted Peter Morter's book "Brownian Motion"? Chapter 8.3. It is explained there that Martin Capacity is zero if and only if the F-capacity is zero (where F is the potential kernel). I guess it only matters whether capacities are positive or zero, so this migh be helpful.