At the end of a session, every player gets 7 XP to spend on his character. Favored entities can be increased without training time, but most other statistics take time and often a tutor to increase. Those who perform useful or particularly entertaining activities related to the game get an extra XP. Those who acheive some special success in-character receive an extra XP. To see how you can spend your XP, check out HouseRulesOnXPCosts. They're very close to the book rules right now. In addition, a character should track Legend Points. When a character performs a legendarily heroic (or heroicly legendary) action, his player rolls the associated virtue and accumulates one Legend Point per success. Particularly anti-heroic actions can cause you to roll the relevant virtue and lose one LP per success. Legend Points are tracked on four scales: Glory (Valor), Mettle (Conviction), Succor (Compassion), and Wisdom (Temperance). Characters start with the 20 LP, distributed at the whim of the player. You can buy the Legend background for your character to get more (see HouseRulesOnBackgrounds). I'd still like to implement a mechanic whereby you need to go tell stories about your Legendary Deeds; the Lunar mechanic of doing so at Face advancement (i.e. Circle advancement) time doesn't quite apply to us. I'm thinking about having LP accumulate "Unsung," and then you go have them Sung and they get moved to "real" LP where you can use them for advancement. Successes on your Performace roll to tell the stories shouldn't modify how many you get, but rather how long it takes to get your Legend spread around among enough people: normal people might need to spend months talking about those Kobolds they skewered, but a Troubadour can do it faster.
This is the official mechanic, but hacking is going on at ExaltedHackingAdvancement