Oh yay! I absolutely LOVE helping people out with hamsters!
-First off, reasearch is very important. It will benefit your understanding, the hamsters needs, and your parents desision. So its a win win win!
-powerpoint or prezi would be a great way to display what you have reasearched. (prezi would be more reccomended since it looks a bit nicer, but its your choice)
-Then, you need to show your parents that your responsible, and can handle your soon-to-be furry's needs. You can do this by helping make dinner, doing the dishes, cleaning your room, (and keeping it clean!) and if you have other pets, then do what needs to be done: walk the dog, feed the animals, clean the litterbox, clean the cages, wash the fish bowl, ect.ect.
-Another great way to show responsibility is making a hamster or pet binder where you store all the basic needs and such.
-Something that really shows parents that your comitted is to save up your money for your hamster. Even if you dont get much allowance or you dont get any at all, save up change, and then you can bring them to a bank or someplace that will exchange your money for bills (5s,10s,20,ect.) In some stores, there are even machines that will do this!
-A little something extra is to bring up facts about hamsters over dinner or breakfast, or even out shopping! Such as "Pine and cedar bedding can harm a hamsters respitory system, just something to know if you ever let me get one." With some parents it works, but with others i doesent.
-one thing I did was make a whole bunch of home-made hamster toys before I got one, so that my Dad would have to say yes, or else they would all go to waste 
-My final, but definatly not lest important tip, is to ask to go to the pet store to see how much it would cost to care for a hamster, and while your doing that, tell your parents to come look at the hamsters and see how fuzzy and hypnotizingly adorable they are!
That is what I did to get a hamster, and would you look at the life he had! Sure it wasnt very full, but it was filled with healthy food, and toys, and love, and happiness. Hope this helped you!