How to find blocks in the pool through “shares” given to miners?

Pools make their members easier targets than the current Bitcoin network targets. Whenever a pool member finds a block with fewer hashes than the pool target, they submit that block to the pool controller to earn a “share.” The pool controller verifies that the hash of the submitted block is less than the pool target and verifies that the coinbase for the block pays the pool controller (or equivalent rule).

So “share” is just a way to track the hash rate each member contributes to the pool.

The mining process is independent of the target. Therefore, sometimes the hash of one of the submitted blocks is not only smaller than the easy pool target, but also smaller than the hard Bitcoin network target, so the pool controller can submit that block to the Bitcoin network and receive the block reward. Payments are made to pool members based on the number of shares each pool member has recently acquired.

The exact details of the pool operation depend on the specific network protocol used by the pool. A widely used protocol is Stratum v2. You’ll sometimes see the submitted blocks themselves sometimes called “shares” or “tasks.” 1 task completed == 1 block submitted == 1 share.