In general, birth control is anything people use to prevent or delay pregnancy so that their family size is planned rather than left to accident. The term "birth control" is often used interchangeably with contraception, but the latter term refers more specifically to those methods that prevent conception during sexual intercourse.
Abstinence and Alternatives
The most basic and cheapest form of birth control is abstinence (not engaging in sexual intercourse at all). However, abstaining from sex entirely can cause great stress and frustration in some people. Thus, many couples opt to engage in oral, anal, or intracrural intercourse or mutual masturbation. However, some either find alternate forms of sex to be unsatisfactory compared to "real" sex or don't wish to engage in them for fear of breaking religious strictures.
Withdrawal is a stop-gap method: the male pulls out of his partner just before he ejaculates. This method requires a lot of discipline on the part of the male and it has a high rate of failure, as sperm can be present in pre-ejaculatory fluid and sperm ejaculated onto the vulva have been known to find their mark. As one of my biology professors noted: "They have a word for couples that rely on withdrawal: parents."
Fertility Awareness
A variation on abstinence is fertility awareness (also known as "natural family planning"). This method involves a couple avoiding intercourse during the times that the woman is most likely to be fertile. Alternately, for couples who are trying to have children, fertility awareness can also be used to improve their chances for conception.
This method requires that the woman be very aware of her own body and her reproductive cycle; some estimate that this method has a 70%-98% rate of success, depending on the regularity of the woman's cycle and the specific monitoring technique used. This technique is different from the much-maligned rhythm method because the woman reads her body rather than a calendar to figure out when she should have sex. Signs that a woman has ovulated (and is therefore fertile) include a sudden change in basal body temperature, changes in vaginal mucus, or a combination of the two.
One advantage of fertility awareness is that it's virtually free and is approved by some religions that otherwise frown upon contraception. The disadvantage is that this method is less reliable than other methods and it requires intelligence, vigilance and discipline on the part of both partners.
Another variation on abstinence that requires less attention to body signs is to have sex only when a woman is menstruating. A woman is extremely unlikely to conceive during her period and for a few days thereafter. The downside to this tactic is that some people object to the mess this can create, and the woman's bleeding makes the transmission of venereal and blood-borne diseases much more likely than at other times. Furthermore, sex during menstruation is taboo in some religions.
Barrier Methods
Barrier methods of birth control work by preventing sperm from reaching the egg. Barrier methods work best in conjunction with spermicides (creams or jellies that contain chemicals that kill sperm and sometimes disease-causing microorganisms). Because barrier methods also prevent the exchange of body fluids to varying degrees, they are also useful in preventing the transmission of diseases; condoms are especially useful in this regard. Barrier methods include:
The disadvantage to barrier methods is that they can be expensive, may not be available to some couples in non-Western countries, can interfere with mood or sensation for some people, and they require correct application. Furthermore, barrier devices are often made of latex, which some people can develop allergies to that can become quite severe.
Hormonal Methods
Other birth control methods work by altering a woman's hormones so as to render her infertile (male hormonal birth control is being researched).
Hormonal methods include:
The advantage to hormonal methods is that they're quite effective and (particularly in the case of long-term methods like Norplant and Depo) require little action on the part of the woman. Another advantage is that for some women with hormonal problems, birth control pills can normalize their systems and cure ailments like severe cramping during periods. The downside is that the methods can be expensive, may not be available to some people, do not protect against diseases, and the hormonal tampering can cause acne, weight gain, mood swings, and possibly cancer in some women.
Furthermore, in women who smoke, hormonal methods can raise their chances of developing heart disease and blood clots that can cause stroke or heart attacks. Thus, physicians usually encourage smokers to seek other forms of birth control.
Interrupting Gestation
Other women may use intrauterine devices (IUDs), which are small "T"-shaped or ladder-shaped devices made of plastic which contain either copper or progesterone. They work mainly by causing an inflammation response in the endometrium that both prevents the fertilized egg from implanting in the wall of the uterus and interferes with sperm motility.
The advantage to IUDs is they're long-lasting (copper-containing devices can last up to 10 years), effective, and the woman doesn't have to think much about them. The downside is they must be installed by a medical professional, can cause cramping and very heavy periods, create an increased risk of ectopic pregnancy, and provide no disease protection. Furthermore, they can sometimes puncture the wall of the uterus and cause life-threatening infections. Women who get pregnant while using IUDs usually conceived shortly before the device was installed.
Other women use abortion (surgery to remove or drugs to induce the expulsion of an embryo or fetus) as a last-ditch effort at birth control. Abortion is a common and ancient practice, and when it is done by qualified medical professionals, it can be quite safe (though complications from any surgery are possible). However, it is illegal in many places and there are many religious and political pressures working against its availability in other areas. Since it invariably involves the destruction of an embryo or fetus, many people are deeply uncomfortable with the idea of having an abortion.
Sterilization
If a couple wants no children at all, they may undergo surgery to render themselves sterile. In women, this procedure is generally a tubal ligation (cutting or blocking the Fallopian tubes, which carry the eggs from the ovaries). In males it is a vasectomy (cutting or blocking the tubes that carry sperm from the testis). These procedures can sometimes be reversed. Hysterectomies and oophorectomies of course also cause sterility, but these surgeries are generally only performed to treat diseases like uterine cancer.
Thanks go out to anthropod for bits to yam for some of the IUD details. Some of the information in this writeup is based on work I did for the science dictionary at http://biotech.icmb.utexas.edu/. The rest was gleaned from memory and various medical texts.