First, get yourself familiar with squash blossom anatomy.
On a male flower, the stamen is the reproductive structure in the center, consisting of an anther (the pollen producer) supported by a thin filament. This phallic anther is what you see covered in yellow pollen grains.
On a female flower, the pistil is the ovule-producing structure, consisting of an ovary (immature fruit) that supports a long style, topped by a stigma (a sticky orange structure in the center). This stickiness is what helps the pollen adhere to it.
During hand pollination, you’re simply mimicking the bees by collecting pollen from the anther and depositing it onto the stigma. Yes, it’s as easy as it sounds!
The ideal time to pollinate squash is in the morning as soon as your squash blossoms open (and temperatures are mild). They tend to close up by early evening, so you might spend several days pollinating by hand if you want to get to them all.