Growing mint plants from cuttings really couldn't be much easier. Simply obtain some mint - you can even use fresh pre-cut mint from the supermarket. You want your pieces to be approximately 4-7 inches long (10-17cm). Cut it just below the bottom leaves. Now pull off those bottom leaves. The area left will be the part you start to see your roots growing from. Now place them in water and leave them somewhere where they will get some light.
Once you notice that roots are forming well in the water, simply pot up, making sure to water regularly initially. It should take around 10 days but may vary due to the amount of light, temperature and type of mint plant.