To find the Thevenin Equivalent circuit between points A and B, all resistances in that section should be combined into a single equivalent resistor, while voltage sources are reduced to one source. The presence of a dependent source requires calculating the voltage across it, which can be expressed in terms of another voltage (vx). Using techniques like Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) or node analysis can help determine the value of vx. Understanding these concepts is crucial for successfully simplifying the circuit. The discussion emphasizes that encountering a dependent source should not be intimidating.