At a typical Earth location, the field intensity is 50,000 nT (nanotesla). How low do you want the shielded field be?
(2) How much effort do you want to invest? Soft iron can shield out magnetic fields, but to shield a relatively large volume (as you want to do) you probably need to use an electric current. For instance, a large pair of coils (“Helmholtz coils”, look it up) can cancel much of the Earth field. You will have to wind them around large plywood frames and probably feed them current from an automobile-type battery. Actually, you may need not one pair of coils but two or three. The magnetic field of the Earth is not horizontal but is inclined downwards (by a “dip angle”), so unless you incline the axis of your coils in exactly the same direction, you will need two or three pairs of coils, with axes perpendicular to each other. You can calculate for each pair the current you need (and hence the number of windings, depending on the wire of course), but in addition you may have to fine-tune the current by using a variable resistor.
