Learning New Abilities

Leaning Skills and Feats
Once a character has enough experience to increase a level, the the character must have an instructor to teach a new feat to increase their skills. The time it takes to learn, is one week per rank gained in a skill and two weeks for a feat learned. A character may work on more than one skill at a time (maximum is the amount of base skill points that your class allows per level) or two feats at once, paying separately for each. Typically it cost 50 gold per week for a professional trainer (plus any related expenses). Ref. DMG page 197

Training Yourself
A character may train them self, but doing so cost double the time and gold cost than hiring a professional.

Learning New Spells
Wizards: Must spend 1 day per spell level, studying to receive their automatic spell from an increased level. This cost is twice as much as if a NPC cast the spell for the character. No roll is necessary to successfully learn the spell.
Clerics: Similar as Wizards, except they pray in service to their patron and donate an equal amount of gold as if an NPC cast the spell for the character.
Sorcerers: Must have contact with a supernatural patron to teach their mortal friend a new spell. Such creature does not care for gold but rather a bargain with the developing Sorcerer.
Bards: They must spend 1 day per spell level, of practicing to receive their spell from an increased level. The Bard must spend twice as much as if a NPC cast the spell for the character for related expenses.
Others: Any other casting type will fall under one of these criteria at the DM's discretion.

Changing a Class or Becoming a Prestige Class
This is not automatic and a character must find a PC or NPC that has that presitge class or class to teach the leveled character new class features in order to become that new class. The leveled character must spend two weeks training in that class the classes first level.

Gaining Hitpoints
Instead of rolling your new hitpoint total per level of the character. The character may opt to take their hit die at half plus one, instead, or may roll and re-roll once. Hitpoints are gained as soon as they successfully trained.