How much area does a yard of topsoil cover?

That depends upon how deep the soil bed is and how much moisture is in the topsoil.

But here are some ballpark numbers for you:

A yard of soil will cover a 10' by 10' area to a depth of three inches. In other words, figure a third of a yard per 100 square feet for every inch of depth.

Length x width x # of inches deep divided by 324 = the number of cubic yards needed for that task.