Audio aids
Very, very complex signal processing, research, and design and goes into commercial audio aids, so a homemade one will absolutely not be able to compete.
A homemade hearing aid would probably just be an audio amplifier. It might probably be:
Microphone->Audio Amplifier Circuit->Speaker
The audio amplifier using the most "regular components" would require an "operation amplifier" IC (Op Amp for short). Read up on amplifiers circuits that use op-amps. You also need to look at a few microphone input and speaker output circuits (which isn't hard, it is almost directly connecting them directly to whatever you need)
It also unlikely to be small enough to work as a hearing aid (seeing as how an IC can already the size of a hearing aid). Hearing aids used specialized chips and such to get them to be small.