There are many ways to generate AM. Historically, the most common form was high-level plate modulation. Now, pulse width modulation is 
much more common. I'm going to try and list what are some of the more common (and some not so common) ways to generate an amplitude 
modulated signal. The following 4 methods are common ways to modulate vacuum tube amplifiers. These 4 are high-level modulation schemes.

Plate Modulation
This method is probably the most common modulation scheme to find in older vacuum tube equipment. It is also probably one of the 
simplest, too. Plate modulation is nothing more than using a transformer (the modulation transformer) to couple an audio amplifier to 
the final amplifier. The secondary of the modulation transformer is placed in series with the high voltage to the final amplifier tube. 
The varying positive and negative voltage devolped across the secondary adds with the power supply voltage to vary the power of the 
amplifier.

Grid Modulation
This method puts the secondary winding of the audio transformer in line with the grid of the final amplifier, instead of the plate.

Screen Modulation
This method, used with tetrodes and pentodes, is just simply placing the secondary winding of the transformer in line with the screen 
grid of the final amplifier.

Suppressor Modulation
Similar to screen modulation, this method is used with used with pentodes and places the secondary winding in line with the suppressor 
grid.


There are a few other ways to modulate a vacuum tube amplifier.

Low-Level Modulation
In this method, the final amplifier is linear. The modulated signal is developed in the lower powered stages, then amplified in the 
final amplifier.

Outphasing Modulation
I believe this is probably the most efficient way to generate AM. Two final amplifiers are used. The phase of the driving signal is 
split so that the 2 phases are 135 degrees out of phase. Each of these phases are then phase modulated and amplified seperately by the 
two amplifiers. The two phases are then combined in the tank circuit that is shared by the two amplifiers, forming the modulated signal. 
The phase of the two carriers will swing so that when the two are 90 degrees apart the carrier is at 100% modulation, and when the 
carriers are 180 degrees apart (cancelling each other out), the carrier is at -100% modulation. There are no modulators used other than 
the 2 phase modulators, so the bulk of the power being consumed is being made into RF, since each amplifier can run with high 
efficiency.

Pulse Width Modulation
This method, unlike the previous methods, is a way that an analog AM signal can be created digitally. The audio source is transformed 
into a series of pulses of varying length. This pulse train is amplified by a modulator tube which turns the final amplifier off and on 
at the same rate as the pulses. This generates the amplitude variations that modulate the carrier.


Nowadays, solid state transmitters are becoming more common. The last three methods I listed can be used to modulate solid state 
transmitters as well as tube transmitters.