for example for DSB-SC/SSB-SC/VSB-SC/QAM you can use the gilbert cell which consists of 8 transistors, for doing the multiplication (the mixer part). you can see the data sheet of the MC1496.
it can also been used for the multiplication part of AM (DSB-LC).
for FM you can see the transistors obviously in any VCO schematics, and VCOs are used for frequency modulation.
if you want AM you need to apply multiplication, which can be done as i told you with the gilbert cell, tis pdf will help you. and the pdf named AN531-D on is very useful too.
we all know what is the role of base in the fuctioning of a transistor. Now suppose the "modulating" signal is applied to base, that will act as an instantaneous biasing to the transistor. This property helps the transistor actually modulate the amplitude of the carrier. whereas what actually happens is you are only changing the instantaneous "gain" of the Transistor Amplifier based on the variations in audio signal.