The basic mechanic for No Higher Authority is diceless TriStat (as seen in The Authority and Silver Age Sentinels RPGS). The GM will do the number-crunching side of character generation and, as in other diceless games, will arbitrate conflict based on straight stat/attribute comparisons and how situations are role-played. A brief definition of the three stats in the TriStat system can bee found over on the character generation page, along with the few other TriStat concepts players might want to be familiar with before play.
The other important mechanic in No Higher Authority is Story Points. Story Points are similar to the objection mechanic from Baron Munchausen, but not as adversarial. Story Points are a mechanism for preventing one players' story from going off on a tangent, leaving the other players bored while the tangent is explored.
Each player starts with 5 Story Points. At any time during the game (especially during someone else's turn), a player can spend a Story Point to add a detail to connect what's happening to something in his or her own “story”. This could be something like Player A saying that his kingdom is at war with another kingdom, and Player B chiming in with the detail that the other kingdom is the one she lives in.
The Story Point mechanic is simple; if you alter the GM's story, you lose a Story Point (represented by small tokens like poker chips). If you alter another PC's story, you give your Story Point to that player. The intent is to encourage players to tie their stories together while allowing in character play to proceed naturally - two characters who might not normally have much to do with each other might find their paths crossing frequently as their players exchange Story Points.
For some examples, see the Examples of Play page.