Steps
Keep busy. Find something to do that is so fun, it will take your mind off of how much you miss your parents.
Write or call your parents often. Hearing their voices or getting a letter for them will make it be more bearable to be without them. If you have access to email, that would work, too.
Internationally usable phone cards are great for any-place travel when you are wanting to call your parents. Just make sure to get the phone card for more minutes than you think you will need; you will always use more than you expect. Also, phone cards are much better than worrying about cell phone charges.
Make some new friends on vacation. Sometimes you can meet the most interesting people when away from home. You could meet a best friend or a new pen pal!
Talk to someone if you feel absolutely miserable without your parents. Whether you're with family members or a friend and her family, no one wants you to be miserable. Talking to someone can help make you feel better.
Find souvenirs for your mom and dad to bring back to them. It can be fun to find special gifts for them, and they will appreciate the gesture.
Know that it will be good for you to more or less fend for yourself without your mom and dad stepping in to fight all your battles.
When you arrive home, don't tell your parents how much you hated your vacation without them, even if that is the case. Talk about the good points of your trip.

Tips
If you just couldn't have a good time without your mom and dad, help them plan another vacation to go on-together.
When you only feel homesick for your parents at night, try listening to some relaxing music or reading a good book to take your mind off of it.
Take some pictures of your vacation spot to show your mom and dad when you get home. It'll be fun to show them what a great time you had.
Have fun! Try not to think about it much. Just enjoy your vacation, and know that your parents will be waiting for you when you get home.

Warnings
Some people try to take advantage of the fact that their parents aren't around, and do things they aren't supposed to. Assume that word of anything you do or say will get back to your parents eventually. Otherwise, you could in big trouble.