Basically, it's a game about making and changing rules, much like actual legislative bodies. Each player proposes a new rule and the other players vote to approve it or not.
Who wins? Whoever reaches the victory condition. What's the victory condition? That'll depend on the rules at the time, which might change in the next turn.
Nomic is a game in which changing the rules is a move. In that respect it differs from almost every other game. The primary activity of Nomic is proposing changes in the rules, debating the wisdom of changing them in that way, voting on the changes, deciding what can and cannot be done afterwards, and doing it. Even this core of the game, of course, can be changed.
Someone to act as the writer while the rest of the group debates and votes should work. Imagine people then fighting over to make rules such that the writer may never type in specific words!
In my experience, the game tends to get very "meta" very quickly. Someone could add a rule that "nobody write down the rules", unless you had the "person X writes down the rules" as an immutable rule, so the moment someone wants to make it mutable... beware!