To find Thevenin resistance (Rth) after shorting batteries, one should use an ohmmeter across the terminals to measure the equivalent resistance seen by the meter. The process involves combining resistors in parallel and series, starting with the parallel combinations of the 4 ohm and 16 ohm resistors, followed by adding the 2 ohm resistor in series, and continuing this method with the other resistors in the circuit. It's important to note that shorting real batteries can be dangerous and is not necessary; the short is a theoretical concept used for calculations. Simplifying the circuit diagram can aid in visualizing the resistor combinations more clearly. Mastering resistor combinations is crucial for efficiently determining Rth in circuit analysis.