Information on fellowship Vitality is a bit confusing, as some of the descriptions were written before DPG reworked the system. Here is how I think it works, based mostly on muddling my way through.
Every toon has two Vitality pools - one for regular XP and another for AAXP. The XP pool can store a fair bit - enough for at least several levels if filled. The AAXP pool is smaller (and more easily filled) and seems to store enough for around 250AA points. You can see the state of your Vitality pools in the XP bars - it shows as a thin green bar on your normal XP and AAXP bars. Shared Vitality is received only periodically (every 15-30 minutes), and you will see a message like "You have received Vitality from your Fellowship" when it happens while you are online. But you do not have to be online to receive it.
Your Vitality pools get filled by others in the fellowship sharing their experience with you. Any character can share (not just maxed chars). If sharing, some of the XP they earn will go into the Vitality pools of other characters that are also sharing. If not maxed they will earn XP more slowly. If maxed already, then the XP would be lost anyway, so no real downside.
Your Vitality pool gets drawn down when you earn experience (i.e., you kill something that gives experience). The increased is significant - you will get several times the amount of XP per kill until the Vitality pool is empty. The effect seems to be multiplicative, as using Lesson will double the total experience per kill.
I am a bit unclear on the following, and would appreciate any confirmation / refutations:
1) To receive Vitality you must be within grouping range of the donors (or above level 85, not clear).
2) You can only receive Vitality if you have sharing on. My prior experiment on this likely flawed, as the toons were below level 85 at the time.
3) When using (drawing down) Vitality it is best to turn off sharing, as otherwise total XP will be reduced if there are any other uncapped characters with sharing turned on.
4) Shared XP is split between recipients, so a single character will fill up pool faster than two.