To build a PC-based oscilloscope using a microcontroller, it's essential to define the specifications such as bandwidth, sampling rate, and input impedance. Resources like Microchip's microcontrollers are recommended due to their built-in ADCs, which facilitate immediate development. The oscilloscope's design will depend on its intended use, whether for digital or analog signal analysis. For digital signals, the focus is on detecting state changes, while analog signals may require continuous sampling or delta change analysis. Understanding the maximum frequency to be analyzed is crucial for determining the necessary sampling rate for accurate waveform representation.