There are lots of options for adults to go beyond the basic training. The next step for fully trained leaders is Wood Badge, a week-long intensive leadership course offered once a year at a council camp. There are also a multitude of opportunities to learn more throughout the year, such as University of Scouting, the College of Commissioner Science, and monthly podcasts from the BSA.
For a more extensive list of training opportunities, see www.scouting.org/Training/Adult
For a youth in Boy Scouting, Varsity Scouting, or Venturing to be considered fully trained and wear the Trained patch on their uniform sleeve, they must take Introduction to Leadership Skills for their program. This course can be facilitated by adult leaders on the unit level and is also sometimes offered at University of Scouting. The next step is National Youth Leadership Training, an outdoors-based intensive leadership development course offered yearly at council camps. From there, youth leaders can go to even bigger training courses like National Advanced Youth Leadership Experiences, offered at national high-adventure bases.
For more information, see www.scouting.org/Training/Youth