Check this out to learn the G major scale in 2nd position. You'll also find several exercises and scale patterns to help increase strength, coordination, and familiarity in this position.
Commit the fingering displayed in the Scale tab to memory. That is the fingering that will be used in all the exercises.
A few notes on how to play the scales and exercises:
Generally, when playing a note with your second finger, your first finger should also be down. When playing third finger notes all three fingers should be down. In time this will become easier for you. This habit is what leads to tremendous speed and dexterity.