@firstch
To answer your OP (in very basic terms):
An Inertial Reference System, IRS, works by you telling it what Latitude and Longitude your aircraft is in the world before starting engines and moving. Then a very accurate system of gyros (either mechanical or laser ring) register any subsequent movement of the aircraft, which the IRS uses to calculate an instantaneous readout of your current latitude and longitude.
An Inertial Navigation System, INS, uses IRS information and the required route you programmed into the flight management system to guide the aircraft.
Modern FMGS use IRS, INS, ground based navigational beacons, and GPS satellite constellations to calculate aircraft position very accurately, sufficient to make an approach to land though cloud with low cloudbase.
The lowest cloudbase and poorest visibility approaches currently available are still obtained from ILS (Instrument Landing System - an integrated system of three ground based transmitters).
You will most likely navigate your Cessna 172 with your eyes looking outside, and by looking inside the cockpit at ground based navigation beacon receivers such as NDB, VOR, DME and perhaps ILS.