Let's talk skin. Acne is ucky. Most people with it wish they didn't have it. It's caused when the the skin's natural bacteria begin to overgrow, feeding on the sebum produced within a pore. Sebum is a waxy material released by the skin in order to keep it soft and impermeable. When bacteria overgrow within a pore, it becomes blocked, and oil and bacteria build up, causing pressure that results in a pimple.
Good skin care is essential to minimizing the appearance of acne. Medications exist, but they all have side effects, ranging from minor (like Retin-A) to huge (like Accutane) and it's best to first try simply taking care of your skin.
Gentleness
The most important thing that you can do to help your skin if you have acne is be gentle! Irritated, inflamed skin is much more prone to developing acne than happy skin. Many (perhaps most) of the acne-fighting products out there are extremely harsh, containing large amounts of alcohol to dry out the skin. This is a very bad approach. While the skin doesn't start to overproduce oil when it's dry (this is a myth created by the skin care industry) irritated skin is much more friendly to the growth of bacteria. Use gentle products. And avoid anything marketed to teenagers: Clearasil products and their brethren, as featured in TV commercials depicting sixteen year olds with skin more perfect than most mannequins, generally contain large amounts of alcohol and other irritating ingredients in order to convince teens that they're 'working'. They will hurt your skin greatly - no one in the world has gotten better skin from a Clearasil product. A lot of them will work great in the short term, clearing up existing zits pretty quickly, but causing more in the long run.
Being gentle means that you should not try to 'dry up' a pimple. Drying the skin weakens its barrier functionality and weakens its immune response, allowing bacteria to grow unimpeded. Being gentle also means not using harsh cleansers. Many acne cleansers contain strong, harsh detergents and irritating ingredients. But acne is not caused by dirty skin, so harsh cleansers won't help.
Consistency
The second most important thing to fight acne is be consistent! You aren't going to 'spot treat' away your zits; by the time a pimple is visible, it's been in the making for two weeks. Thus, careful, gentle, consistent treatment is key to combating pimples. When your skin is smooth, you must continue to treat it, and when it's broken out, resist the urge to use harsh products.
There are four main aspects to skin care for someone with acne: cleansing the skin to remove oil, removing dead skin cells, reducing excess oil, and killing the bacteria. In addition, there are various drugs that are used in more serious cases.
Cleansing
Basically, you need a gentle cleanser, and if you're acne-prone, it'll generally be one formulated for oily skin. Make sure to avoid any irritants - if the cleanser is abrasive or contains menthol or similar ingredients, it will irritate your skin, and even if the irritation isn't obvious it increases the skin's propensity to break out. The best cleansers are ones with no fragrance, as fragrances are the cosmetic chemicals most likely to cause skin irritation or sensitivity. Irritated skin is more hospitable to bacteria.
Exfoliating
The top layer of skin is composed of dead skin cells slowly being pushed out from the bottom by new tissue growth. Exfoliation means assisting the very uppermost layers of dead cells to slough off, either mechanically (many exfoliants are essentially gritty substances like ground peach pits and the like) or chemically.
Generally chemical exfoliants are most useful for skin care; mechanical exfoliants are liable to cause tiny injuries to the skin, abraiding it and hurting its barrier function. For acne, salicylic acid, also known as beta hydroxy acid (I have a brief node at that location), is the best option, and it's a common ingredient in over-the-counter acne treatments. It's the only exfoliant that enters the pores and acts within them. Because it is oil-soluble, it can dissolve in the sebum filling the pore and remove the dead skin cells inside the pore that build up and block it. In addition, BHA has anti-microbial properties and may help reduce inflammation and redness.
An easy and cheap mechanical exfoliant, though, is baking soda. Make a paste out of a little bit of it and skin cleanser, and (gently!) rub it over your wet skin, making sure to rub every par of your face. Don't go overboard - you can cause your skin to get all red and hurty.
Excess oil
Not only does oil on the skin look ucky, but it encourages the development of acne. If your skin is particularly oily, it may help to remove excess oil. Avoid products containing alcohol - although ethanol will very efficiently remove oil from the skin, it is immensely irritating and damaging to the skin and will hurt the skin in the long run. Clay masks or products containing magnesium hydroxide will absorb oil, improving the skin. They must be used fairly frequently - every couple days or even daily for real greasy folks (I don't even want to think of how goddamn oily my skin was when I was a teenager.) Pure milk of magnesia purchased from a drug store works quite well, and is much cheaper than most masks that are available in stores. Apply a thin layer, let it dry, wash it off.
Disinfection
Since bacteria are the cause of acne, reducing the number of them is a great idea for improving the skin. Benzoyl peroxide is the most common chemical to do this, and is available in numerous over the counter products. Most of them seem to have a 10% benzoyl peroxide concentration, but as the stuff is irritating, this amount can hurt your skin, eventually worsening the problem. Look for products with a concentration of 2.5% or 5% and work your way up to 10% only if it's necessary. And be warned - it can bleach clothes, bedsheets, and so forth; one particularly hot day, my sweat ended up bleaching part of a shirt.
The next step
Come up with a skin care routine that addresses all of the steps needed to fight acne and try it out for a few weeks. If it doesn't work, you might need to try out what pharmacology has to offer.
Accutane
Accutane is a harsh, though effective, pill that dries up the skin and will often cure acne for life after a six month treatment. It has some unpleasant side effects, however - and if you're of the female persuasion, you'll be required to learn all about the godawful birth defects it'll cause if you get pregnant. The doc will demand a pregnancy test, you'll be required to use some sort of birth control, and you can't donate blood if you're on it.
Antibiotics
Some people take oral or topical antibiotics to combat the bacteria behind acne. This is also a fairly strong approach and thus not a first resort, but it can make a big difference for some people.
Birth control pills
These are only an option for women. Excess oil production is caused by hormones, and certain birth control pills can make a big difference in some cases. Controlling the hormones from the inside is the only real way to affect oil production. Of course, some women will experience worse skin from some birth control pills. It might be necessary to try more than one.
Tretinoin
Tretinoin, sold as Retin-A, is a vitamin A derivative that can treat problem acne. It's applied topically; it penetrates to the dermis and changes the way cells grow. It is quite irritating for some people but it may also minimize the appearance of wrinkles.
Differin
Differin (adapalene) is another retinoid - like tretinoin - but some people find it less irritating or more effective.
Azelaic Acid
Yet another topical prescription drug used to treat acne, azelaic acid may be more effective that adapalene or tretinoin, and is considered the next step up.