When the t-handles are perpendicular with the pipe it's in, the valve is closed/off. When the t-handles are parallel with the pipe it's in, the valve is open/on.
For usage, you want the cold water inlet valve open (parallel with pipe), the hot water outlet valve open (parallel with pipe), and the bypass valve closed (perpendicular with pipe).
For bypassing the heater in the winter, you close both the inlet and outlet valves...but open the bypass valve (which let's anti-freeze bypass the hot water heater)
The picture you have above has every valve in the closed/off position, which is what is probably causing the confusion. I think it is just to show you the valves, not their correct position for summer/winter.
You need to open the hot and cold valves, but leave the bypass valve closed. Like the top picture here: