There are a lot of factors involved with this.
1. Tutoring. This is understated. Can't stress how much important this is. If they are Professional, or tutored to reach Professional personality, then it will help them grow tremendously, even only from just Reserve matches. They grow exponentially faster than those players w/o similar personalities. Meaning, you can mostly give them Reserve time, with occasional cup games, and even then, around 20, they'll be ready for first team action.
2. Squads. Have a glance, and try to place your brightest prospects (irrespective of age) in your U21s, and the rest in U18s. Meaning, have a look, and place future first teamers in your U21s. In U21s, they get trained by your first team coaches, the matches are tougher and they develop better. Don't overcrowd it, else they won't get gametime.
3. Game Time. Again, vitally important. Give them cup-games for the first couple of years, till they turn 18-19. I tend to play my cup games with mostly my youth squad, with a couple of experienced players thrown in. IF you don't want to take that kind of direct risk, have them in subs. When they're around 19-20, the most promising ones - those who should have developed enough to challenge for first team should ideally be in your subs for the PL. Introduce them into CL a year or so later.
4. Training. First, when you get the youngster, determine their playing position. Then, have a peek at that particular position. From 15-17/18, I'd say it'd be beneficial to give overall training, covering a wide range of attributes for the roles required. Alternate that with Physicals - whichever are needed for the role. After 18, you can alternate with specific role training along with technicals. Around 20, cover their weaknesses, if it already hasn't been addressed till date.
5. Loaning. This can be a double-edged sword. You only want to loan out under specific conditions. The facilities of the club should be excellent or higher. Also, the players should atleast be a first teamer, in a preferred position. I only tend to loan out those players, who should already be first team material (rotation or higher) in my team, but have other players in front of them. These players can go out, make an impact in the loanee team, and develop well.
There are lots more stuff which matters, but the core basics I tend to follow are these. I managed to create WC youth players this way for United. Ofc, this was back in FM14, but I don't think the core principles have changed all that much.