Firstly and foremost, masturbation is a completely normal, healthy activity to do. No one should feel guilt or embarassment from masturbating.
Simply put, masturbating means sexually stimulating oneself (yourself) - usually until an orgasm is reached. An orgasm is an incredible, intense feeling of pleasure and it does not hurt.
Teens who masturbate should do so in the privacy of their own are (whether it is the bathroom or the bedroom or otherwise). This is because, like many sexual activities, masturbating is a private act.
Of course, some things differ between boys and girls.
Masturbation for Boys
Boys have been known to masturbate daily (and even multiple times each day).
The common method of masturbating for guys is rather simple: gripping the penis with one hand and moving the gripped hand up and down along the penis. Some boys find that switching hands during masturbating reduces hand fatigue/soreness. The use of moisturizing lotion or lubricants may increase the feeling of pleasure for some boys.
Depending on a boy's development during puberty, he may experience something called ejaculation while having an orgasm. Ejaculation for males refers to semen coming out of the penis. Some boys will ejaculate in a squirting manner (spitting), while other boys will ejaculate slowly (dribbling). As a side note, the more frequent a boy masturbates, the less semen he will have to ejaculate.
After an orgasm, a male will usually have a calm or tired feeling - males cannot have more than one complete orgasm without a significant amount of time before the next orgasm, which means that guys cannot have multiple orgasms.
Male masturbation is also known as: jacking/jerking off, beating off, beating meat, wacking off, and wanking. For example, "Tom said that he caught his brother jacking off yesterday."
Masturbation for Girls
Although it is more common for boys to openly talk about it, girls masturbate about as often as their male peers.
Unlike boys, girls can masturbate by using one (or a combination) of several techniques. Rubbing the clitoris (a small peice of skin right above the vagina) is one of the most effective techniques. Some girls may also insert one or two fingers into the vagina to stroke the G-spot. The G-spot may be hard to find, but it is usually found about 2 inches within the vagina (on the top-side). Stimulating this area is very pleasurable, and some girls describe a slightly different, but not lesser, feeling than rubbing the clitoris. The overall experience of masturbating can also be increased by massaging/rubbing the breasts.
Girls may also ejaculate during orgasm, however, the fluids usually go unnoticed. Of course, fluids that may be ejaculated from a female do not contain sperm.
Another advantage that girls have is the ability to have multiple orgasms. Some girls find it normal to have several orgasms while masturbating.
Female masturbation can be called fingering or rubbing one (or more) out. For instance, "Jessica told me that she rubbed one out as soon as she got home."
Masturbation/masturbating is sometimes mispelled as "masterbation", "masterbating" and even "masterbaiting". Although this shouldn't confuse too many people, it should be noted that it's all the same thing with just spelling issues.
Also, remember that masturbating is completely normal - even as frequently as multiple times a day. As long as it does not become an obsession, it is mentally and physically healthy.
Surveys and discussions can be found in the: Puberty 101 Forums.