The skills that you see are the integer part. So instead of 3.7 you will see "awful". When you train, a player's skill will improve. If it improves from 3.7 to 3.9, it won't be visible, though the player will perform better. When it improves from 3.9 to 4.1 you will see "inept" and a little green arrow. The green arrow will remain until next week's training.
Also, each training regime does not affect just one skill. Even something like "rebounding" will also improve the "inside defense" skill, so you might see some green arrows there as well.
You will on rare occasions see a little red "down" arrow. Mostly this will indicate a drop in stamina, which happens for all players. It can also be a drop in another skill, but this will only be for older players (30+).
You won't see an arrow for changes in game shape or experience.