To be able to train and develop players in the Youth Academy, you will need to upgrade Youth facility in the Ground menu to at least the first phase. However, note that as you continue to upgrade your Youth Academy facilities, new slots for young players will become unlocked, until you reach the maximum (4 slots).
Facility upgraded to level 0 - 1st slot for young player unlocked
Facility upgraded to level 3 - 2nd slot young player unlocked
Facility upgraded to level 5 - 3rd slot young player unlocked
Facility unlocked to level 10 - 4th slot young player unlocked