I want to build a Frequency Modulation circuit
There are lots of ways to do these things.  One easy way to think about amplitude modulation is to make a oscillator, then have another signal vary its power supply.  You don't say what you want to modulate with what kind of signal, but amplitude modulating a square wave is particularly easy.  If you want the carrier to be a sine wave, then you can filter after the modulation to reduce the harmonics.  If you are modulating at a fixed carrier frequency, then a resonant output filter will get rid of most of the harmonics.

FM modulation is also easy, but a little harder to conceptualize if you're not fluent with electronics.  There are chips that do this, called voltage controller oscillators, or VCOs for short.  One way you can do this yourself is to note that a capacitor charges up more quickly thru a resistor when the voltage at the other end of the resistor is higher.  You can make a oscillator out of this, where the period is set by how fast a capacitor charges up and discharges.  The more current you supply for the capacitor to do this, the faster the oscillator will run.  The 555 timer is based on this principle of charging and then discharing a capacitor to different theshold voltages.  With a little cleverness, you can have a modulation signal change how fast the capacitor is charged and discharged, which in turn effects the oscillator frequency.

This can be done digitally too.  For FM, use a hardware PWM generator built into a micro, and adjust its period based on the modulation signal.  For AM, a hybrid approach is possible.  Many D/A converters are ratiometric to some reference signal.  This means the output is really the product of the analog reference voltage and the digital value.  This can be used to perform AM.  If the signals are slow enough, you can compute the final output and write that to a fixed D/A.

There are many other ways too, both for AM and FM.  If you explain more specifically what you are trying to do, a more specific answer is possible.