Gay: Same-sex attraction. Sometimes used as an umbrella term.
Bisexual: Attracted to same and different genders.
Transgender: Identifying as a gender different than the gender assigned at birth.
Questioning: The process of questioning one's sexual orientation or gender identity.
Queer: A once derogatory term which as been reclaimed by the LGBT community. Sometimes used as an umbrella term ("the Queer Community") or as an identifier ("I'm queer").
Asexual: Lack of sexual attraction.
Pansexual: Attraction regardless of sex or gender identity (often overlaps with bisexual).
Intersex: A variety of conditions in which a person is born with an anatomy or chromosomes that don't fit the typical definitions of female or male. (Note: Not all intersex people consider themselves part of the LGBT umbrella.)
Non-Binary: Gender identities that do not to a strict masculine/feminine binary. (Related: genderqueer, agender, genderfluid.)
Note: With the exception of lesbian, all the above terms are only used as adjectives. So saying "a transgender person" or "a queer woman" is acceptable, while "a transgender" or "a queer" is not.