First find the region in the xy plane where the function intersects the x and y axes. Looks like a triangle in this case. Then set the interval for the outer integral, say x from 0 to the x-intercept. Then the interval for the inner integral is from y=0 to y as a function of x. Find this function by setting z to zero and solving for y. Then evaluate the partial integrals starting from the inner integral for y. For fun, switch the order of integration, as is allowed by Fubini's theorem.
Hey, we just went over all this in my Calc class so it is fresh in mind!