For positive character traits, it needs to be in the range (the top portion of the green, there is a line demarcation) where they will receive the trait when they age up.
Scouting badges are earned by doing normal things. Click on the board and Badge Progress (you might need to hover over to see the tooltips) and it will tell you what they need to do to earn them - friendly and funny socializing, arts and crafts, physical, outdoorsy, mental, etc.