Since pools only receive successfully calculated shares they must approximate your actual hashrate based on the number of shares submitted.

Assuming we're talking about difficulty 1 shares, you should be able to approximate hashrate via H = S * 2^32 / T where H = hashrate, S = shares submitted and T = time in seconds. Your estimate will be more accurate for larger values of T.

It takes approximately 2^32 hashes to find a share and each share has a 1/D (D = difficulty) chance of correctly solving the block. From that, with some simple math, you should be able to calculate almost every important thing about mining.