Think natural beauty. Make everything look fresh and elegant.
Nails: Light pink or just clear polish would look wonderful. Also, make sure that they are clean and filed down to an appropriate length. French Manicures look fabulous and can make a girl look classy and elegant. Whether it's a home DIY nail session or at a professional salon, you should always try to have good nails.
Make up: Apply it on carefully, but make sure not to overdo it and look too garish. Take care to make it look fresh and natural. Fun colors every once in a while are a good idea too, but don't apply them all at the same time so that you look like a clown!
Hair: It doesn't have to be done in high curls or tight ringlets. Just make sure that it's moisturized nicely and combed. A cute up do when it's hot outside can look super classy. Make sure you have a good hair care routine too - shampoo it, condition it and apply creams to get it as pristine as possible.
Clothes: Choose clothing that suits you and your taste. But be careful; you do not want to appear tomboyish. Also make sure the clothing you pick is clean and stain-free. Also, be modest! Being a princess means dressing like a lady. You do not have to show off.
Never sacrifice comfort for style. A princess should feel at ease in all situations. Now, this doesn't mean show up at a formal dinner in a tracksuit, but know that when you are comfortable, people will be comfortable around you!
And most importantly....
A Princess is a princess inside and out. So while you may look the part of a princess, you must make sure that you always portray a princess inside as well.
It was interesting to study the contrasts on what the conceptions of a "princess" were between the two "-hows" - there's the rest of this guide at wikiHow and then a different one at eHow. The latter list is a bit pretentious (it's for adults) and reminds me more of a spoilt step-sister instead of a proper lady, yet this is what passes for one today...