The mandolin is commonly played with a pick (or plectrum). Picks come in various sizes and thicknesses. Generally the thinner ones work better for rhythm playing and the thicker ones are better for melody playing. You may need to experiment with several picks before deciding which one suits you best. The traditional picking grip is to hold the pick between the thumb and the last joint of the index finger.
To pick the strings, use a downward motion of the pick (called a downstroke and indicated by the symbol (a ), and use only the tip of the pick to strike the string, as shown in the diagram.
Use the tip of the pick to play the string.