To get a steady feel and sound it is important to anchor your hand. The best way of doing this is by placing the thumb on the top of the pick-up (see photo).
You should also experiment by playing with your thumb resting on the back pickup, as the sound is clearer and has more attack and "bite".
When playing notes, the rest stroke is used. The rest stroke involves the finger picking the string and then coming to rest on the next string. The following photos illustrate the movement of the index finger in playing the rest stroke. I.e., pick the A string and come to rest on the E string.
Alternate between your index and middle fingers. Anchor your thumb on the pickup and strike the open G string with your index finger in the same fashion as with the rest stroke technique. As soon as it comes to rest on the next lower string (D string) pick the open G string again, this time using your middle finger. Maintain this alternating movement between the two fingers. Make sure one of the two fingers is always resting on the D string while the other one is picking the G string and vice versa.
Always use this alternating finger style as it will give you more possibilities when changing between notes and strings.