When you are finished training with a trainer, you make a roll similar gaining an Ascension Skill Point.

Training with a trainer is a 100% success, as you gain higher skill tiers it becomes more difficult to gain or takes longer to train with the trainer.

The main difference is with training is you ALWAYS add your Mind (either plus or minus) essence during the d20 to roll higher than your current skill tier. This rewards "smarter" player characters who can learn faster, and can be beneficial to train at higher tiers.