How do block rewards work with a mining pool? I understand there are a number of different schemes for sharing rewards. 

My question is about the block reward itself, and how it's shared.  If only one miner (typically a pool) can find a reward, that means that a pool doesn't get a reward for every block processed.  Yet somehow, the miner is still paid, even if no block is found.

Are all the shares submitted between blocks found counted?  ie.  If a pool finds a block every 10 blocks, do the shares from the other 9 get added together and the entire block reward split across all work done on the found and previously unsuccessful blocks based on the share scheme?
As others have said schemes differ. But to try to answer the question you asked:


  Are all the shares submitted between blocks found counted? ie. If a pool finds a block every 10 blocks, do the shares from the other 9 get added together and the entire block reward split across all work done on the found and previously unsuccessful blocks based on the share scheme?


Probably not. That would be a terrible scheme. Assume a pool has a constant hash rate. Right after it has found a block, it's just as likely to find another block in the next minute as it is when it hasn't found a block for a long time. But the reward per share will be much higher if the pool finds a block shortly after finding another block and much lower if the pool hasn't found a block in a long time.

So a pool that counted every share since it last found a block would likely see a huge influx of users right after it found a block, since the expected reward per share will be abnormally high.

And if the pool is unlucky and hasn't found a block in a long time, the number of counted shares will be abnormally high, making the reward abnormally low. This will cause miners to abandon the pool.

So counting all shares since the last found block is perhaps the worst reward scheme possible.