Here are a few ideas - some may work for you, others may not.
You do need to prove to your parents that you are serious about getting a dog and not just asking for something you won't be taking care of in a few months time anyway....
Do you get pocket money? Save it up.
Make a pot and put it in your room (where they will see it) - give it a big, obvious label "Dog Fund"
Put all your pocket money in there. Don't spend money on candy or other toys. Don't try to save for anything else.
Don't ask for new clothes, toys, new DS games or other sneakers, etc.
Ask your parents if you can get some money if you do chores around the house, like cleaning the kitchen floor or clearing the driveway of snow, etc.
Tell your parents they get to choose what chores you do. Don't just offer to do the ones you are prepared to do. Do anything
Put the money you earn in your Dog Fund pot.
Get a crate and de-clutter your room of toys - have a "yard sale" of your old toys - put the money you get in your Dog Fund pot.
If you are asking your parents to spend a lot of money on a dog and supplies you have got to show them you are seriously interested and prepared to save up yourself if necessary.
It may not come to that of course... they may decide to "help you out" with some money if they see that you are serious about saving yourself.
