This can be done in various ways depending on what equipment you have access to. If you have used JavaTC the software design program to aid you in your construction, you will already have a rough idea of the resonant frequency and where you need to tap the primary coil.
In this case you can get the final tuning point by continually testing different tap points close to the estimated point, and see which gives the best results. Using a Variac in the input to the HV source helps because it means you can then run the coil at a lower power. Turn the variac too low though and the NST will not output enough volts to fire your spark gap however.
The reason for initially running it at a lower power is that if the coil is badly out of tune and run at full power you can cause damage, either to the secondary coil, the capacitors, or in some instances the HV power source.

If you have not used JavaTC then now may be good time to get it and use it on the coil you have built, or else calculate the resonant frequency yourself. Use Google to search for various sites giving all the formula's.



You will need to work out the resonant frequency of the secondary first of all. Then you work out at what point you need to tap the primary's spiral so that the resultant inductance that the tap point gives, combined with your capacitance value, will result in a resonant frequency that matches that of the secondary minus around 5% to 10%.
The reason for deducting a small amount from the secondary's frequency is that when a streamer breaks out from the Toroid, the capacitance value alters and the secondary's resonant frequency drops by a small amount. The figure will vary from coil to coil and also on the distance the streamer is jumping.

As an extreme example, on my own coil when arcing to a grounded rod just 2 foot away the frequency dropped from 140 down to an amazing 110Khz! In this instance though the coil was at full power with the grounded rod connected by wire to the RF earth. Normally the coil will do 38 inches so the 24 inch test resulted in a thick full power arc.

A big advantage in using an oscilloscope and a signal generator (as explained below) to tune your coil, is that you can make a more accurate allowance for the effect that the streamers will have.
You will however most likely need to fine tune manually to finish things off.



(Above) Tuning the Primary
The 10K (approx) resistor is very important so don't forget it. Without it the scope is just sitting across the generator's output, so it will only see that voltage and not the coil's.







(Above) Tuning the Secondary



The instruments are connected as shown above. You will then need to have the signal generator set to an initial frequency that is about 30 to 40 Kc/s within your expected resonant frequency. You then gradually increase the frequency whilst watching the oscilloscope display.
At some point the voltage that the 'scope is measuring will sharply increase. Just how suddenly this occurs can be affected by the coarseness of the signal generator's tuning dial. I modified my own so that I had quiet fine tuning in the range of 100 to 200 kc/s (other coils may well resonant higher or even lower than this range).
You may find that there are several points where the voltage increases, but there will always be a dominant one that is more than others. This voltage peak can be seen in my YouTube video clip below





'YouTube Video of Tuning a Tesla Coil"


When tuning the secondary it a good idea to add a piece of wire hanging down from the Toroid to simulate a streamer. The length of this wire should equal half to one whole length of an expected streamer. If you have never run the coil be realistic in deciding how long a streamer is likely to be, otherwise you are defeating the object of doing the exercise. A little bit of time spent tuning initially will mean you can expect your coil to work reasonably well when you first fire it up. The primary should be tuned without the secondary in place. While the secondary can be tuned while it is mounted on the coil so long as the spark gap is not shorted. So if you had previously been tuning the primary you must remember to remove the link before doing the secondary! I have tried tuning the secondary both with and without the primary in place and on my own coil there is little difference, as can be seen in the first two results below.

The remaining three results attempt to show the simulated effect that streamers might have. Secondary Coil Results:

Freq =	233.1 Khz	(No Primary, No Toroid, Secondary Coil on base)
Freq =	231.6 Khz	(with Primary, No Toroid)
Freq =	148.1 Khz	(with Primary, with Toroid, No streamer)
Freq =	135.9 Khz	(with Primary, with Toroid, with 1 streamer)
Freq =	127.8 Khz	(with Primary, with Toroid, with 2 streamers)

The last but one reading above of 135.9 Khz is the frequency that I chose to tune the primary too. This represents the most likely scenario with the coil running. It is obviously not correct for when the coil first fires up with no streamers formed yet, and neither is correct for multiple streamers, but it is a suitable compromise or 'average', from which I can then manually tune.
The first two results of the above table show that there is little significant difference between the secondary being tuned whether the primary is in place or not. Half a turn on my primary coil equals a change in frequency of 4Khz, so the difference between the two readings of just 0.5 Khz equals 1/16 of a turn. As it is always necessary to manually fine tune a coil anyway, this is something that you will sort out.


A Circuit to view the resonance.



This circuit is attributed to Antonio Carlos M. de Queiroz and can be found along with a lot of other very interesting stuff on his site Here.. Antonio suggested using a 1 ohm resistor across the spark gap but I found I needed a 0.5 ohm to be able to see the correct waveform. The frequency from the signal generator must be square wave and needs to around 1 to 4 Khz for best results.