... the computer takes that measurement and compares it ...
This may happen with large aircraft, where the computer adds in temperature, humidity, pressure altitude and Angle of Attach to compute a direct reading of "calibrated" airspeed, but most aircraft don't employ a computer. Instead, a simple diaphragm attached to the airspeed needle in the instrument casing separates two chambers, one filled with ram air, the other with static air. The pressure differential between the two chambers flexes the diaphragm, which in turn rotates the needle, and the resultant reading is "Indicated" airspeed, which throughout most flight regimes is within a small enough percentage of true airspeed to be a useful indication of "attitude" or "angle of attack".
Airspeed is not a useful gauge of groundspeed: that can only be determined by timing the passage between two points of known distance, since winds aloft can significantly reduce or increase speed over the ground. Airspeed is instead, especially in light aircraft, used as an indirect indication of "attitude", AKA "angle of attack", since low airspeed is closely correlated with high angles of attack. The airspeed indicator is therefore mostly ignored until setting up the landing approach, where target airspeeds are used to establish the proper descent rate, and to prevent the airplane from being inadvertantly slowed to the point of stall.
Airspeed is of no use to establish cruise setting, as engine power is the determinant for cruise - the airspeed winds up being whatever it is once the desired cruise power is set (that is, a pilot does not adjust engine power to reach a target cruise airspeed, instead power is adjusted to meet criteria of fuel consumption, engine longevity, and the airspeed that results is the cruise airspeed for that flight. Aircraft weight will affect the resultant airspeed at any given power setting - and as the airplane burns off fuel it will slowly gain a knot or two of increased airspeed).
Back to the pitot tube: except for very light, slow aircraft, pitot tubes are extended outward so as to be clear of the compressed boundary air (or "bow wave") of the moving aircraft, and thereby pick up their ram air undisturbed by the aircraft.