Summarize:

Arrange a time to sit down with your parents and ask for the money. You want your parents to know that you aren't taking this situation lightly, and you'd only be asking if you needed it. You'll come across as more serious and sincere if you set up a time beforehand, rather than having a quick phone call or just casually asking for the money in passing. Depending on how large a sum you're asking for, you might want to bring some paperwork to your discussion with your parents. Show them how you calculated the exact amount that you need. Indicate how much you've been able to save to pay for the item, then ask for the remaining amount.  If you're asking for money for a specific item, find it online and print out the price. If you'd like extra money you can use as a cushion, be upfront about that. Tell them that if they give you a certain amount now, you'll be able to get on your feet and won't have to ask again. If you're going to pay them back, you might want to provide a printed installment plan or schedule they can keep. This shows that you're serious about making good on your promise. You probably have a fairly good picture of what your parents' finances are like. Still, it's better not to assume they can give or even loan you a large amount of money. Ask them if they feel comfortable with the amount you're asking for. They may tell you they simply can't afford it, or that they'd be able to give you a partial amount. Asking for money is a big favor, and your parents are entitled to making a few stipulations. They may say that they'll give you just a part of what you're asking for, or perhaps they'll say they can loan you the money if you pay it back within a short time. Your first inclination might be to get upset or angry that they didn't give you what you wanted with no strings attached. However, if you want or need the money, you'll have to accept what comes with it.  It's possible that your parents will decline to give you the money. If that's the case, see if there's anything you can do to make them feel better about giving it to you. Is there a chore or job you could do in exchange for the money? See if you can make repairs, do the grocery shopping, or help out in some other way. If they still won't budge, don't beg. Instead, try to find another way to get money. If you show your parents you're resourceful, they may even decide to help you out. If your parents decide to give you the money, it's in your best interest to tell them thanks. If you're over eighteen, your parents are no longer obligated to support you financially, so the money they hand over is a gift. If you want to go above and beyond, you could even write them a thank-you note. Your attitude will make them feel more willing to help you out in the future.
Have a polite conversation. Lay out your plan. Make sure they can afford it. Accept their stipulations. Say thank you.