There are data sheets for all three devices readily available. The data sheets describe how to connect and use them. I think you're going to need to add a PIA to the 80188 for the interface.
These are very old components, so this must be a school assignment.
I'm not familiar with the 80188, but it should need an interface chip. That would be the PIA (parallel interface adapter). It sends data through that to the D to A converter. Using a low pass filter, the output of the converter goes to the 324 (or part of it - it's a quad op amp) and then the buffered and amplified analog signal drives the 386, which has enough poop to drive a speaker.
Read up on everything and come back if you have some specific questions.
Try a passive filter between the DAC and the amp. A cap & resistor in series to ground across the amp input might shunt out the sharp transitions from the DAC.
You need a low pass filter between the output of the DAC and the input of the op amp. The DAC output switches from one state to the next very rapidly, which is where the noise is coming from. The filter will smooth out the rapid transitions and make the sound quality more acceptable. Most audio DAC's are 16 bit, so your audio is never going to sound really good.