Opening the book…
To measure something you must interact with it, and interaction is mutual: the probe exchanges energy or momentum with the system, so reading a value generally changes it. A voltmeter draws some current, a thermometer absorbs some heat, a pressure gauge admits some gas. This is ordinary physics, not mysticism; the disturbance is a real coupling between instrument and system that follows the same conservation laws as everything else.
Ask what your instrument takes from the system to produce its reading, and estimate that against the quantity you want. A good measurement is one whose disturbance is negligible: use a voltmeter with resistance far above the circuit's, a thermometer with tiny heat capacity, a probe that samples little. When you cannot make the disturbance small, model it and subtract its known effect, or infer the undisturbed value by extrapolating to zero probe influence.
In quantum mechanics the disturbance becomes fundamental rather than merely technical: non-commuting observables cannot both be sharpened without limit, and the act of measurement projects the state. That bound survives no matter how gentle the apparatus.