Pollinating flowers on pumpkins and squashes is a common thread on here and a quick search yields a ton of results.. that said, here's a run down:

Pollinating: as with any fruit, some pollen needs to reach the stamens in the female flower in order to pollinate. pumpkins are not self pollinating (unlike say a tomato) and have seperate flowers for pollen and ovaries.

Sexing flowers: Male flowers are usually long stemmed and won't have a small fruit at the base. Female flowers usually have short stems out further along the vines but most importantly, if you look at the base of the flower you'll see a small fruit if it's female and nothing is there if it's male. You can also tell the difference looking inside the flower but checking for the fruit is the easiest way to tell them apart.

Note: pumpkin flowers are only viable the same day and usually only until about mid-day. after the flowers start to close up, if the flower isn't pollinated it's probably game over for that fruit.

Here is a link that might be useful: pollinating pumpkins

This is a close up of the center of the male flower. It will be on a long skinny stem. Most likely the bees and other insects will take care of pollinating for you but if you want to be sure this is how I do it. If I have plenty of males I will cut the stem right from the vine leaving enough to hold on to. Then I carefully cut or tear most of the blossom away from the stem leaving the stamen (with pollen attached) If you do this early in the day it is best as much of the pollen will still be on the stamen. Then gently touch the stamen to the center of the female flowers to pollinate. If I have few male flowers I will just use a Q~Tip to transfer some of the pollen from the male to the female flower. It does not take much.

Here is the inside of the female blossom. You can see the difference from the male right away.

This is a picture of the female blossom from the side. You can see the small pumpkin under the blossom. As planetes stated above, your blossoms male and female will be open for a limited time. If I plan to pollinate by hand I will be checking every day to see what will probably open the next day. I does not take long to recognize blossoms almost ready to open. Good luck! Have fun.

deebee~ rereading your post I notice you have your vines growing up a trellis. I don't know how big your pumpkins will get but the vines will not support the weight of pumpkins over a few pounds. I have not done it but have read about many who have made a sling of sorts to support the pumpkins weight so they don' tear from the vine. I have heard of old t~shirts, pantyhose, sweat-pant legs etc. cut off and opened up and tied to the trellis on either side of pumpkin leaving plenty of room for it to grow.

Here is a link that might be useful: Pumpkins on a trellis