First step is to work out which category you fit into....
People who are transgender can usually be broken down into one (or more) of several categories:
Crossdressers: Previously known as "transvestites," this group of individuals is content with their birth gender, but chooses to dress up as and use the mannerisms of the opposite gender. Crossdressers clothe themselves in the clothing of the opposite gender not for the purpose of entertaining others (as drag performers do), but because they feel more comfortable dressed as such. Note that crossdressers are NOT necessarily gay, nor do they necessarily want to undergo sexual reassignment; it is purely a choice they make about how to dress.
Drag performers: Drag performers, the male half of which is sometimes referred to as "drag queens," are individuals who dress up as and use the mannerisms of the opposite sex for the purpose of entertaining an audience. Think RuPaul. Some drag performers identify themselves as transgendered, and some do not.
Transsexuals: This group of individuals was born into one gender but identifies emotionally and psychologically with the other. The medical term often used to describe this situation is "gender dysphoria" or "gender identity disorder." The complexities of this state are numerous, and people in different stages of their "coming out as a transsexual" process may refer to themselves in very different ways. Male transsexuals may choose to use hormones, have surgery, or do neither in order to live as women. The point is, these are people who feel that they were born in the wrong body and will often do anything they can to remedy it.
Intersexed: An intersexed person is someone who was born with ambiguous genitalia, so doctors assigned him/her a specific gender at birth. Sometimes this assignment doesn't correlate with the biological XX or XY gender. These children are socialized as a certain gender, but as they grow older, they might not necessarily identify as they were assigned and would want to switch to the opposite gender.
Gender-blenders, androgynes, etc.: This group is made up of people who identify as transgender but do not fit themselves into any other category that we list above. They may wish not to constrain themselves to these gender categories and will live with aspects of both male and female genders.
Remember that people who identify as transgender may date men, women, both, other transgendered people, or no one at all.