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Dear Ms. Lanes,
Dear Dr. Brown,
Always use Ms. for a woman unless you know that she
prefers Mrs. or Miss. If you can't tell from the name whether the
person is a man or a woman, it is acceptable to use the person's full
name in the greeting, although it's better to find out their sex first:

Dear Terry Carlsan,
Terry Carlson, if he's at all aware of the problem, should
sign his name Mr. Terry Carlsan when he responds to you, to end
the confusion. Americans don't usually use the British method of
Terry Carlsan (Mr.), but it's a nice solution.
If you don't know the name of the person you are writing
to, for example because you are writing to a company to complain
about something, use "Dear Sir or Madam":

Dear Sir or Madam
I am writing to complain about the service I received in
your restaurant yesterday.

If you are responding to a letter that someone sent, start by
thanking them:

Dear Mr. Johnson,
Thank you for your letter of July 1.

When ending a business letter, close with "Yours truly" or
"Yours sincerely":

Yours truly,
Alan Parks

If you started your letter with "Dear Sir or Madam," you
are supposed to use "Yours faithfully," but most Americans don't -
they still use "Yours sincerely," or just "Sincerely" if they want to
seem very serious or slightly angry.