Watch the Basic Right Hand Technique online guitar lesson by John Goldsby from Upright Bass Handbook
The thumb of your right hand should be lightly anchored on the edge of the fingerboard, towards the bottom end of the fingerboard. This position allows you to pivot with your right hand and pluck notes on all four strings with equal momentum.
I think of plucking the bass with the right hand as a motion generated from the wrist and fingers. Any wrist motion starts with the upper arm and shoulder, but those are big muscles. For the delicate task of playing pizzicato--plucking the string in other words--we need to use the fine motor skills of the wrist and hand. I can pluck the string with one finger, my index finger. Or, I can use two fingers together in tandem to pluck one note. Or, I can alternate index and middle fingers to play faster passages or rhythmic embellishments. More about those techniques later.
When I'm walking quarter notes, I'll usually play with my right-hand index finger. I think of striking through the string. I believe that a big sound and good tone comes from the speed that your finger travels through the string. I don't pull the string and let it snap, rather I strike through the string in rhythm. This gets a strong attack and a long sustain. This motion starts with the wrist, and follows with the finger playing through the string. I like to compare this motion to dribbling a basketball or like a drummer's stick hitting a ride cymbal in a repetitive rhythm.
It's also helpful to think of using my right hand index finger in a small circular motion to pluck the string. The slower the tempo, the larger the circular motion. The faster the tempo, the smaller the circular motion. My right hand motion is in time, and the motion determines the sound and the groove.
Now here's a disclaimer: If you see ten different bass players, you'll see ten different ways of plucking the string. I think you should experiment with the techniques that I'm showing you, and use your ears to tell you what sounds and feels the best. Everybody's body is different; we all have different physical profiles that we deal with when we play the bass. The various types and sizes of double basses also might require different techniques. You're the ultimate judge of which of these techniques is for you by using your ears.
Now it's your turn! Play some open strings and listen to the sound. Try to get a flowing motion with your right hand, and pluck each string over and over and let it ring. Sounds good, doesn't it? Let's move on to some open string exercises in the next lesson.