To achieve a counter that counts three clock cycles using the 74193 or 74191, preload the counter with the value 3 (binary 11) and count down to 0. For counting up, the counter should increment from 0 to 2 before resetting. It's important not to use the carry signal for reloading if the goal is to stop the count after reaching 0. A schematic has been drawn, but confirmation of its correctness is needed for proper implementation. The discussion emphasizes the need for clarity on whether to count up or down and how to effectively reset the counter.