Sketch the shape described in the problem. This is often on an "xyz" coordinate system, but the problem may also be given in cylindrical or spherical coordinates. If this is the case, use your formulas for converting between coordinate systems if it is easier for you to work in another coordinate system.
Find the limits of integration with respect to x, y, and z. Sometimes, these are given to you in the problem, as in problems which simply state: "The solid is bounded by y = 0 and y = z + 2." Other times, you will have to isolate the variable in question in a given equation, as in a problem using the ellipse 4x^2 + z^2 = 4 and giving no explicit limits for z in the problem. In this case, the equation rearranges to z = + or - sqrt(4 - 4x^2), and the z-values run from the negative value to the positive value.
Write the triple integral, ordering dx, dy, and dz in the order you think it will be easiest to integrate them. Sometimes you may end up with an integral that you cannot integrate when doing this. If this is the case, start over with dx, dy, and dz in a different order. Don't forget to write the limits of integration in the integral, keeping track of which order the x, y, and z limits are in so it matches the order of dx, dy, and dz starting from the center and working outward.
Integrate three times, working from the middle outward. Apply the limits of integration after each integration. If the answer involves pi, leave pi in the answer; do not multiply by an approximation of pi or 3.14.