You install a 30-amp breaker box by wiring it to a 30-amp, double-pole breaker in the main panel. If the sole purpose of the subpanel is to increase the capacity of the main panel, you can install the two panels side by side, but if the panel is servicing remote circuitry in the garage or in the far side of the house, you'll have to run cable through walls or possibly underground. It's important to run the cable properly to guard against ground faults and sheathing deterioration.
Cable to Use for Remote Subpanel Wiring
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You need 10-gauge, three-conductor cable to wire a 30-amp subpanel. This cable has two hot wires (usually colored red and black), a white neutral wire and a ground wire, which is usually bare but could be green. It carries electricity at 240 volts, so you must treat it differently than regular 120-volt electric cable.
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If you're running the cable underground to a garage or outbuilding, you have two options, depending on how deep you're willing to dig. If the ground is hard and rocky, and it's only practical to go down 6 inches, you must enclose the wires in rigid galvanized conduit, and instead of a single sheathed cable, you need to run individual wires. The other option is to dig a 24-inch trench and direct-run waterproof UF-B cable. This cable must be enclosed by PVC conduit at depths less than 18 inches, so you need to bury vertical lengths of conduit at either end of the run. They should have appropriate waterproof fittings to attach to the main panel and to the subpanel or to the side of the house and the side of the outbuilding.
Subpanel Neutral and Ground Buses Must Be Separate
A panel enclosure usually comes preequipped with two hot bus bars, a neutral bus and a ground bus. The neutral and ground bus are usually joined, and the panel comes with a screw that you install on the neutral bus to bond it to the metal enclosure box. The neutral and ground buses must be connected and the bonding screw installed if it's a main panel. Since it's a subpanel, though, the neutral and ground bars must be separate, and the neutral bar can't be bonded to the enclosure. This ensures that all grounding occurs at the main panel. Otherwise, ground-fault devices on circuits controlled by the subpanel wouldn't work.
Sometimes, the ground and neutral bus are joined by a bonding strip but are otherwise separated. If so, all you need to do is remove the bonding strip and discard the bonding screw. If the neutral and ground bus bars are permanently joined, you must install a separate ground bus. Most panels have predrilled lug holes for this purpose. Again, throw away the bonding screw. You don't need it.
Making Wire Connections
Inside your 30-amp subpanel, you'll find lugs on the bus bars for each of the incoming wires. The red and black wires go on the hot buses (usually brass), the white wire goes on the chrome neutral bus and the ground wire goes on the ground bus.
Inside the main panel, you'll need two adjacent slots in which you can install a 30-amp, double-pole breaker. Connect the red wire to one of the breakers in the set and the black wire to the other, and then snap the breaker into place. It doesn't matter to which breaker you install either of the wires. Connect the white wire to the neutral bus and the ground wire to the ground bus.
Be careful. The main breaker is always energized, even when the main breaker is off. Do not touch either of the hot bus bars with your tools. It's best to wear rubber-soled shoes and rubber gloves for protection when making panel connections. If you're not confident doing this job, do not hesitate to hire an electrician.