To find the Thevenin equivalent circuit for a circuit with a current source, first determine the voltage across the terminals, specifically across the 5I_x element. Nodal analysis is suggested as an effective method for this process. By applying a load impedance ZL at the output, the output node voltage can be expressed in the form Vo = V_{th} (Z_L / (Z_L + Z_{th})). This may require some manipulation of terms to isolate Vth and Zth. Understanding these concepts will facilitate the conversion of a current source circuit into its Thevenin equivalent.