How does a bicycle pump with pressure guage actually work?

Your question seems to focus on the accuracy of pressure gauges. Many economy pumps add a gauge for marketing purposes (you'll get what you pay for). This doesn't mean the high end pump gauges are necessarily better however. Consider buying your pump and gauge separately with the requirements you need from each in mind. Pumps have different applications: some are designed for size and weight (bicycle mounting), others for pressure and/or durability (shop use)). The volume of air required to fill an automobile tire is so much greater than that required for a bicycle that the time and effort involved usually requires a motorized pump ((but a bicycle pump will work). Gauge accuracy also depends in part on application. Most automobile tires are inflated to 30psi +/- 10psi, bicycles range from 20-90psi, other uses are lower and higher. Gauges can be designed for pocket sized convenience or accuracy ((Bourdin tube). Take your time and review what's available.