How it works:
From left to right, the first part is the microphone and some resistors to get it working. Next we have a capacitor and the first transistor, this amplifies the sound from the microphone so that it can be loud enough to work with. The last part, there is a transistor, a coil and some capacitors. This part generates the radio waves and combines them with the sound from the mic to transmit it thru the antenna.
The coil is made with about 9 turns of wire, use a pencil to get the right diameter for the coil. The capacitor with the arrow is called a trimmer capacitor, it has a small screw to adjust the value, we'll use it to tune a certain frequency or station to transmit on.
(click to enlarge)