An example of the TeslaTronix solid state Tesla coil circuit board:
The resistor or potentiometer leads from V+ to the base of the transistor, and the reverse facing diode also leads from the base of the transistor node to ground.
The terminals for L2 are soldered together as one node, so you can connect the L2 to either terminal. L1 terminals ARE NOT soldered together. L1 is in series with V+ and the collector node. One benefit to having 2 terminals is the ability to easily add and remove an additional secondary, or L3. The voltage at this node will also excite a second tower if enough input current is present.
The driving circuit itself is tiny, and with enough ingenuity, you can probably get it to fit on a PCB the size of a quarter! Solutions can easily be made etched, or not etched on standard project board.. or of course on any breadboard. Actually, it is recommend to assemble your circuit first on a breadboard. A good heatsink is key. Never run your circuit without a heatsink. Would you run your desktop PC without a heatsink? Increased longevity and increased input voltages are also advantages of a large heatsink properly secured with thermal paste. Preferably, the heatsink should be positioned parallel to the base, to keep it from absorbing high levels of feedback from the L2/C.