Two squash bees and a cucmber beetle had already gotten busy inside this flower.
Next find a male flower from the variety you want to be the papa. Male flowers have no small green fruit underneath (just stem) and the inside part is just like a post.
You can just pull this male flower off and tear the petals off so that you can poke the yellow pollen covered post from the center of the this flower into the female flower and smear the pollen all over the parts in the center of that female flower. It's as easy as that! Wait for a squash to form and at least some of the seeds should be the hybrids you wanted. Some will be from the work of the squash bees.
Now if you want to do a "controlled" cross (so all the seeds will be the cross you want), you'll need to keep the flowers closed from the night before so the bugs can't get into them. I've used masking tape or coils of wire (like toys come packaged with) to keep the flowers closed before and after my hand crossing.
I've tried a simplified method yesterday evening with an unopened 'Delicata' squash female flower. I don't know if it'll work but I went ahead and ripped open a male flower from one of my hull-less seeded squash lines. I pried open the 'Delicata' flower bud and put the anther column from the male flower inside, in contact with the stigmas. I went ahead and sealed it shut - tied with grass. The flower never actually opened but I'm hoping that anther column released it's pollen onto the stigma anyway. I'll let you know how it goes.