If winding your own coil then you may find Martin E Meserve page very helpful:
Single Layer Air Core Inductor Design
An alternative is to use a toroid core of appropriate material. Toroid's come in different sizes and colours, see the sample below.
A T130-2 core requires approximately 137 turns of 36 SWG wire.
Mike Yancey has a very useful Toroid calculator on his webpage, link below:
The circuit is in two parts, a microphone pre-amplifier built around Q1 and an RF oscillator circuit (Q2). The oscillator is a standard Hartley
oscillator which is tunable. Tank circuit L1 and C1 control frequency of oscillation,
the power in the tank circuit limited via emitter resistor R1. The transmitter output is taken from the collector, L2
and C2 form another tuned tank circuit and help match the antenna. L1,L2, C1 and C2 may be salvaged from an old AM radio if available. The antenna
should be a length a wire about 10 feet or more. In the schematic I have shown coaxial cable to be wired to the "longwire" antenna, the outer coax
shield returned to ground. Ground in this case is a cold water pipe, however even without a ground and coax cable a signal should still be possible.
L2 and C2 not only help match the antenna to the transmitter, but also help remove harmonics and spurious emissions in the transmitter circuit
caused by non linearity in the transistors.
Q2 needs regenerative feedback to oscillate and this is achieved by connecting the base and collector of Q2 to opposite ends of the tank circuit
which is achieved by C4. C3 ensures that the oscillation is passed from collector, to emitter, via the internal base emitter resistance of the
transistor, back to the base again.
Emitter resistor R1 has two important roles in this circuit. It ensures that the oscillation will not be shunted to ground via the very low internal
emitter resistance, re
of Q2, and secondly raises input impedance so that the modulation signal will not be shunted.
Q1 is wired as a common emitter amplifier, C7 decoupling the emitter resistor and realizing full gain of this stage. Bias of this stage is
controlled by R4,R5 and R3. The microphone is an electret condenser type microphone, R7 setting operating current of the ECM and C6 providing DC
blocking. The amount of modulation is controlled by the 10k preset resistor PR1 which is also the collector load. The preamp stage is decoupled
by R6, C8 and C10. This ensures no high freqency feedback from the oscillator gets into the audio stage. Some electrolytics capacitors have a
high impedance at radio frequencies, hence the use of C10, a 10n ceramic to bypass any oscillator frequencies.