Connecting transmitter coil to the oscillator
Connecting the coil to the oscillator is easy.

The coil goes from the point marked "Output" to the ground of the transmitter circuit.

Getting more power is trickier.

Your circuit uses the 2N2222 transistor both as an oscillator and to provide power to the coil.

Rather than messing with a circuit you've found on Youtube, I would recommend starting over with a better circuit.  Pretty much any circuit has to be better.

The existing circuit doesn't let you vary the frequency of the transmitter.  You need to do this to hit the resonant frequency of the inductor/capacitor (LC) resonant circuit formed around the coil and its companion capacitor.  If your oscillator isn't running at the resonance frequency, then you will lose a lot of power in the transfer. The oscillator might be built so as to oscillate at the tank frequency, but given that you are asking how to attach the coil I expect you have taken an oscillator circuit from somewhere and are trying to use it to drive your (not matching) coil.

You could add an amplifier to the existing circuit, but that's just throwing more power into it without making things really better - you will still be throwing away a lot of power.

For this to work, you need three things:


Transmit and receive tank circuits with the same resonance frequency.  You appear to have coils with the same inductance but you seem to have different capicitors to go with them.  The receiver and the transmitter will therefore have different resonance frequencies.
An oscillator that runs at the resonance frequency of the tanks.  Your oscillator runs at some frequency which may or may not be close to the resonance frequency of the tanks.  It has no simple way to change the frequency, even if you knew what frequency is needed.
Power.  The 2N2222 is a small signal transistor.  It doesn't want to deal with the current it would take to transfer large amount of power.  It will burn out before you get significant amounts of power through the coil.


I suggest starting over with a circuit for a system in which all of that has been considered.



This question on this site goes into detail of a very simple system 

Resonance of the tanks is covered.

The oscillator is built such that it naturally oscillates at the resonant frequency of the tanks.

It uses a much beefier transistor that will allow more transmit power.

Then there's this site  which appears to be someone's homework or class assignment.

It goes into some detail about the theory, and provides a system that works.

It uses a separate oscillator that you tune to the resonance frequency of the tanks, and an amplifier to provide more power to the transmit coil.

Either of those would work better than what you've got.

I recommend reading the text in both links.  It is all good information about how wireless power works.