I am wondering, if a man gives a sperm sample to be tested for fertility treatment or similar, how do they count the sperm? I mean, they are tiny and there can be 100 million+ in a sample, so presumably they do not have a machine which counts all of them? Do thye count a tiny sample manually under a microscope and if so, how do they know the rest of the sample is the same?

They count sperm the same way they do bacteria, etc... under a microscope. There are a certain number of sperm per volume of fluid as an average per man. The volume of sperm per unit in seminal fluid is what determines fertility of males.

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The normal volume varies from 1.5 to 5.0 milliliter per ejaculation. The sperm count varies from 20 to 150 million sperm per milliliter. At least 60% of the sperm should have a normal shape and show normal forward movement (motility).

When a man produces a sample of seminal fluid, it is caught in a container. By the time the sample is examined, there is a fairly even amount of sperm distributed throughout the sample.

Semen Analysis