First of all, don't panic. You've done the sensible thing and asked for help.
Secondly, you're not alone. Millions and millions of women have facial hair, but not very many talk about it.
Thirdly, take your time in thinking about this. There are any number of people giving out misleading information and plenty of people ready to take money off you while offering "cures" that don't work or are virtually useless.
This is a problem you've got to divide into two sections -- medical and cosmetic.
To deal with the medical side first of all, if your periods are regular and you've got normal breast development and no obvious physical abnormalities other than facial hair, then there's probably nothing to worry about medically. If you suffer from irregular periods or have anything else out of the ordinary medically (apart from the facial hair), you should definitely have a check-up in case you have something like PCOS.
Beware of a doctor suggesting that you go on to birth control pills -- they do increase your estrogen levels, but they lower your natural production of estrogen which may not rebound quickly or at all when eventually you stop the pill, so your end situation can be worse, rather than better.
Now, as far as the cosmetic side of things is concerned, this is where you've got to go carefully.
If there's not too much facial hair, do you really need to do anything? Most guys are OK about women with, for example, a slight moustache.
If you do decide you have to do something, then there isn't a simple answer.
Facial (and also body) hair on women comes about in the same way as on men because of
1) your body being sensitized, before you were even born, to testosterone -- doesn't happen to all girls, but does to many
2) your body producing high levels of testosterone
The growth rate and coarseness of the hair depends on just how much testosterone is circulating in your bloodstream.
Steer clear of bleaching -- when someone sees you against the light you'll look as if you have a glowing moustache and/or beard.
As far as removing it is concerned it's worth remembering that
* Waxing, plucking, threading, epilating all pull the hair out by the roots and where the growth is hormonally-driven can actually stimulate a dormant follicle into producing more hair quicker. They also distort the root if done repeatedly, leading to hair growing at strange angles. And you've got to let the hair grow to quite a length before you can repeat the exercise. It can also damage the skin and discolor it. Long-term use of waxing also causes bad wrinkles.
* Chemical depilatories strong enough to remove the hair are very likely to burn the skin, cause swelling and cause long-term discoloration of the skin.
* Laser is also liable to cause burning and discoloration and in any case only works effectively on a dark hair/light skin combinantion. Laser can only work long-term if your hormones are within normal female range.
* Electrolysis is very liable to cause scarring and discoloration of the skin. Electrolysis can only work longterm if your hormones are in the normal female range.
Which, like it or not, leaves shaving which does not damage the skin. Best done with a men's-style electric razor, the best of which, for women, are probably those from the men's range of Norelco razors (Philishave outside the US). Most women who try a men's Norelco wonder why nobody ever told them about it before.
Most guys are quite OK about a girl who shaves, as long as she's open about the fact. What they don't like are girls who are in denial about the fact that they've got facial hair.