P2Pool miners are paid every time a block is found by the pool for any confirmed shares they currently have in the P2Pool sharechain.
This is known as a Pay Per Last N Shares (PPLNS) payout system, and is the mechanism P2Pool uses to both determine payouts and discourage pool hopping. In P2Pool the N in PPLNS is 8,640 for most coins. Each of the last 8,640 shares are paid each time a block is found. A share in the P2Pool sharechain can be expected to last between 1 to 3 days depending on the coin.
Confirmed shares are valid, and paid whenever a block is found, for as long as they remain in the sharechain. Payouts in P2Pool are made immediately, directly from the block generation transaction. All payouts are paid directly into your wallet which you have designated as your miners UserID. Payouts are paid each time a block is found by the P2Pool network.
As a miner on P2Pool you are competing with other P2Pool miners for a portion of the 8,640 active shares. The more shares (and the higher the difficulty of those shares) you have in the sharechain, the greater your reward when a block is found.