The most common way of playing the guitar is 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 lead 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.
The correct position for your right arm is demonstrated in the following photo. Notice that your forearm rests on the upper edge of the guitar, just below the elbow. Be careful not to have your elbow hanging over the face of the guitar, or your right hand too far along the fretboard. Also when you are playing single notes, you can support your right hand by placing the second and third fingers on the body of the guitar.