I willo only add to CrazyEye's answer that the improvement doesn't necessary mean a green arrow next to a skill, improvement can be only few sublevels, which is not visible except you can check that their DMI changed, that means training update took place and game shape and skills are updated. (theoretically DMi could stay the same but that's very unlikely) Such an improvement doesn't go away, you are jsut closer to that green arrow in next weeks.
And of course, players have to play minutes on trained positions to receive training (except Team trainings - Stamina, free throws and game shape trainings).