Light, Medium, and Heavy Training will only allow you to increase a stat to 850. Advanced and Ultimate Training will allow you to reach the actual game stat cap of some ungodly number.
Training your Strength and Agility will use energy, determined by the level of training you use.
Each level of training has 2 options, one for Strength and one for Agility.
Ultimate Training requires you to be level 300 or greater, with at least 850 Strength and 850 Agility, and you also must have a Jewelled Medallion.
In addition to training stats, you can also increase them by using Nectar or AP, by praying for stat increases using Faith Points from the Shadow Church, or by converting Master Diamonds or Master Emeralds in the (optional) Clan Castle "Character Upgrade Shop.