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Your power supply transformer determines how large you can make your Tesla coil. Most Tesla coils operate with a transformer that puts out a voltage between 5,000 to 15,000 volts at a current between 30 and 100 milliamperes. You can obtain a transformer from a college surplus store or from the Internet, or cannibalize the transformer from a neon sign. The best way to create this capacitor is to wire a number of small capacitors in series so that each capacitor handles an equal share of the total voltage of the primary circuit. (This requires that each individual capacitor have the same capacitance as the other capacitors in the series.) This kind of capacitor is called a multi-mini-capacitor or MMC.  Small capacitors, and their associated bleed resistors, can be obtained from electronics supply stores, or you can scrounge for ceramic capacitors from old television sets. You can also make the capacitors out of sheets of polyethylene and aluminum foil. To maximize the power output, the primary capacitor should be able to reach its full capacitance each half-cycle of the frequency of the power being supplied to it. (For a 60 Hz power supply, this means 120 times each second.) If you're planning on a single spark gap, you'll need metal bolts at least a quarter-inch (6 millimeters) thick to serve as the spark gap to withstand the heat generated by the discharge of electricity between the sparks. You can also wire multiple spark gaps in series, use a rotary spark gap or blow compressed air between the sparks to moderate the temperature. (An old vacuum cleaner can be used to blow the air.) The coil itself will be made of wire, but you'll need something to wrap the wire around in a spiral shape. The wire should be enameled copper wire, which you can obtain from an electrical supply store or by cannibalizing the outlet cord from a discarded appliance. The object you wrap the wire around can be either cylindrical, such as a cardboard or plastic tube, or conical, such as an old lampshade. The length of the cord determines the inductance of the primary coil. The primary coil should have a low inductance, so you'll use comparatively few turns in making it. You can use non-continuous sections of wire for the primary coil, so that you can hook sections together as necessary to adjust the inductance on the fly. This completes the primary circuit. As with the primary coil, you're wrapping wire around a cylindrical shape. The secondary coil must have the same resonant frequency as the primary coil for the Tesla coil to operate efficiently. However, the secondary coil must be taller/longer than the primary coil because it has to have a larger inductance than the primary coil, and also to prevent any electrical discharge from the secondary circuit to strike and fry the primary circuit. If you lack the materials to make the secondary coil tall enough, you can compensate by building a strike rail (essentially a lightning rod) to protect the primary circuit, but this will mean that most of the Tesla coil's discharges will hit the strike rail and not dance in the air. The secondary capacitor, or discharge terminal, can be any round shape, with the 2 most popular being the torus (ring or donut shape) and the sphere. This completes the secondary circuit. Your secondary circuit should be grounded separately from the grounding for your household circuits supplying power to the transformer to prevent a stream of electric current from traveling from the Tesla coil to the ground for your household circuits and possibly frying anything plugged into those outlets. Driving a metal spike into the ground is a good way to do this. Chokes are simple, small inductors that keep the pulses created by the spark gap assembly from wrecking the power supply transformer. You can make one by winding thin copper wire around a narrow tube, such as a disposable ball point pen. Place the primary and secondary circuits next to each other, and connect the power supply transformer to the primary circuit through the chokes. Once you plug the transformer in, your Tesla coil is ready to run. If the primary coil is of sufficiently large diameter, the secondary coil can be set inside it.

Summary:
Choose your power supply transformer. Make the primary capacitor. Design the spark gap assembly. Build the primary inductor coil. Connect the primary capacitor, spark gap assembly and primary inductor coil together. Build the secondary inductor coil. Make the secondary capacitor. Attach the secondary capacitor to the secondary inductor coil. Build the pulse chokes. Assemble the components.