A min/max thermometer is a typical thermometer with a couple interesting changes. First, it has been bent into a U shape for convenience in reading. Also, the liquid does not extend down into the bulb at the low-temperature end like most thermometers. Because the liquid does not fill the bulb at the low temperature end but instead is free flowing, minimum temperatures are easily determined.
Your min/max thermometer should have a marker at each end of the column of mercury. As the temperature drops, the column of mercury will move up the left column towards the bulb. This movement will push the marker up the left column as well. Then as the temperature increases, the mercury will move away from the bulb end. This will push the other marker up in the direction of the top of the right column.
These markers will indicate the minimum and maximum temperatures between resets. These markers are often held in place by magnets, so you can reset them by using the magnet included with the thermometer.