Pick the male flower early in the morning. Male flowers grow on long, thin stalks. Male and female flowers will only bloom for one day and then will die, so morning pollination is important.
Pull all of the petals off the flower taking care not to damage the anther, a solid, tube-like structure at its center. You also want to ensure you don't dislodge pollen before you reach the female flower.
Locate the open female flower. Female flowers grow on short stalks, close to the vine. You'll be able to see the immature straight neck squash between the flower and the vine.
Dust the stigma in the center of the flower with the male anther. Dust gently so you don't damage the stigma. The stigma is easy to locate, it will be the only thing in the center of the female flower.