There are two main approaches to generating AM:
1. Generate the AM signal at a low level (power/amplitude), and boost it to the required output power via linear RF amplification, or
2. Generate the AM at the final power level by directly modulating the gain/amplitude of the final (Class-C i.e. non-linear) RF power amplifier.
There are pros and cons of both approaches and which technique you choose will be influenced by the required power levels, frequency response, audio fidelity and the devices to hand. By way of illustration, here's a simple AM audio transmitter I cobbled together using an ancient 1 MHz TTL oscillator (which consumes the bulk of the operating current shown!) as the frequency determining element. (I've used the second approach to AM modulation in this circuit - also known as "plate modulation" from the old valve transmitter technique of modulating the anode [plate] voltage of the output amplifier).