FIRST- DO NOT ATTEMPT THIS IF SOMEONE IN YOUR HOUSE IS ALLERGIC TO DOGS OR IF YOUR PARENTS/GUARDIANS WORK FULLTIME!!!! Think about what you want in a dog- do you want it to be active/lazy, large/small, intelligent/dumb, etc. Make a list of options, including breeds you like, and what gender you prefer. Lots of internet sites have info on breeds characteristics.
Step2
Talk to your parents/guardians and ask them if the options you have written would be suitable for a dog in your household. Ask them reasons why they don't want a dog, and if possible, what would make them let you have one. Try to do everything you can to make them happy, maybe if you do well in school they'll see that you are responsible. You could even take up extra chores or tasks around the home. If you have other pets, take up full responsibility for them.
Step3
Now you should ask for a dog. Your parents should say yes, if not, keep trying, but don't be rude or cheeky, just hint or ask politely. Good Luck.
Tips & Warnings
THINK ABOUT THE EXTRA RESPONSIBILITES OF OWNING A DOG- IT TAKES COMMITMENT AND DETERMINATION. MAKE SURE YOU READ UP ON IT.
NEVER ATTEMPT THIS IF YOU HAVE MORE THAN 4 OTHER PETS- IT'S NEVER GOING TO HAPPEN.