In the binary representation of the hash. Now the hash should be about 80 zeros. In the share - less, but how much exactly? At the dawn of bitcoin in a share, it was enough to have 32 zeros. Now the difficulty has greatly increased.
What are the share requirements for popular pools?
First of all, Bitcoin does not actually use the number of zeroes for the difficulty. Rather it interprets the hash as a number and checks that the block hash is less than or equal to a particular target. This makes the hash have several leading zeroes, but those zeroes are not being considered directly.
The target for a share varies by pool, and usually, by miner as well. Miners can choose a target that matches their hash rate so that they aren't submitting shares too quickly or too slowly. Of course the shares are weighted by difficulty (i.e. target). So a share with a higher difficulty (lower target) is worth more than a share with a lower difficulty (higher target).
Most pools offer setting the difficulty to many values. For example, Slushpool lets you set it anywhere between 128 and 500,000.
Each difficulty is associated with a target hash, which is a 256 bit number.
For example, for diff 1.0 the hexadecimal target hash is: 0x00000000ffff000000000000000000000000000000000000000000000000000 which has 32 binary leading zeros.
As long as difficulty increases, the target hash decreases according to the formula:
current target = first block target / difficulty = 0x00000000ffff000000000000000000000000000000000000000000000000000 / difficulty
Finding the appropriate method to perform such division you can calculate the target for any desired difficulty and know the number of leading zeros.
Regarding mining pools, as the previous answer said, it depends on the miner, the hash rate, the pool... what difficulty you can or you are going to be using. Slow miners will likely use lower difficulties, so according the previous formula their required target hash is not too small for their hardware to still be capable of finding hashes that are less or equal than the target. Fast miners can calculate more hashes/sec, so they will mine at higher difficulties with smaller target hashes.
