Factors that affect the speed of specific training (in no particular order, all are very important):
1) age like HockeyArena or Hattrick. Because players need to be more welll rounded in this game I do continue to train talented players as old as 22, if they have good secondary skills. They'll be the first one I sell though. Training is highly affected by age (see below). 16-19 is VERY trainable (based on talent of course) 20-21 pretty good, 22-23 ok to train but not really optimal, 24-27 doesn't train hardly at all, 28+ starts to skill decline... ALL YOUR TRAINEES SHOULD BE 20 OR YOUNGER IMHO, when you start out.
2) Talent- Hidden attribute of the player - For now you'll be guessing, and if you find players that aren't training well, DUMP THEM and buy new ones.
3) Skill level - low skills rise faster
4) The skill of the head coach in the stat being trained. Main coach: needs to be "unearthly" in the skill being trained. High rating in relevant secondary skills do help, but too expensive for new teams. As you win games, fill and upgrade your stadium and promote, you'll be able to afford better coaches.
5) The GENERAL APPRAISAL of your THREE assistant coaches. Specific skills are irrelevant, it's only the general appraisal that matters. Can't have more than 3 assistants, shouldn't have fewer. For now all should probably be solid or so, they're cheap.
General training: all players who played in a game receive it. Trains slower than specific but allows for improvements in skills that are not being trained specifically. Similar to specific training, is dependant on age, talent, skill level, skill of head coach in each other stat, and gen appr of assistants.
Very important that you know that only general appraisal matters:
1) Start with an excellent youth coach when you get 2-3 "keepable" players for your youth squad.
2) Only keep youths that will reach "solid/very good" skill coming out of the school based on a guess of about 5 weeks per pop. You'll be able to find out the talent as they progress. Ignore the first pop - they could be JUST before the next level so they could pop in 2 weeks the first time and still be talentless. 3.3 is just about the fastest training ever recorded (max talent), 4-5 is pretty good, 6-8 is pretty bad. With your coaches it will be much slower, those #'s are based on outstanding or so youth coach (3.3 was with magical)
3) Timing is important, when you have a few players coming out at about excellent/formidable upgrade to an outstanding/incredible youth coach. You can have your youth graduates pay for your better Youth coach and you can even keep the talented