How would I protect my hardware from unwanted magnetic induction?
Lightning is an example of a current pulse that can cause strong enough magnetic fields to damage electronics. I've seen even relatively insensitive components such as resistors damaged (not a direct strike, but nearby so that current is induced in wires). 

You can protect it by limiting the voltage and current. For example, a lightning arrestor and spark gap arrestor might limit the voltage to a thousand volts (the first by shunting massive current away, the second a much smaller current, through some series impedance), then some series resistance and a TVS might get you down to 50V, a voltage which your electronics could be designed to withstand.  

If your equipment must withstand extreme EM fields (near a radio transmitter) or extreme magnetic fields (for example near an MRI machine) you do have to take precautions. Induced voltage and even the a high enough DC field can result in damage. 

Magnetic shielding doesn't work all that well at room temperature, and shielding high intensity fields at low frequencies can be remarkably ineffective. For example, mu-metal has a nice high permeability for fields in the tens of \$\mu T\$ (like the weak field from the Earth), but will saturate and be little better than air if exposed to a significant magnetic field. Lower permeability materials (such as iron or ordinary steel) can be used to shield the mu-metal. 

Generally, the kinds of magnetic fields that are found in ordinary circumstances don't induce a lot of voltage in random spots, and there is enough impedance present that damage is unlikely. You do occasionally see some disruption or degradation of operation, such hum in an audio amplifier or 60Hz pickup in a thermocouple signal conditioner.