If you read the datasheet and application notes for the LM386, you'll get some guidance in how to do this. Moreover, you may want to pre-filter your MCU output before it gets to the amplifier in order to improve the tonal quality. (requires some reading!)

How do you intend to construct your waveforms? Do you plan to use PWM? (more reading!)

Do you know what an integrator is? Do you know how to build one with an Operational Amplifier? Have you considered how that might help this particular assignment?

You could use a single transistor in an emitter-follower configuration. That wouldn't be very good, though. While a single transistor provides either a source or a sink it isn't push-pull, hence can't drive a speaker very satisfactorily. (more reading yet!)

With a larger power supply (~12 volts) and TWO transistors, you could do some interesting things. The op-amp verison is something you could finish within this life, however.

If you can't obtain the LM386, then search the web for "complementary emitter follower." The LM386 is normally quite inexpensive, though, and if you want to succeed, that's probably the "easy" way.

RE