Here is a quick rundown of the different DNA tests and what you can find out with them.
mtDNA
(mitochondrial) is the female line DNA that is passed from a mother to her children.
Everyone, male or female, carries mtDNA and can be tested but males don't pass it along to their
children. Only females pass it along. mtDNA can connect people on your mother's mother's mother's
(etc) line and can show the distant ancestry of your strictly female
ancestral line.
yDNA
is carried only by males and only males can be tested. This traces your
father's father's father's (etc) line and can help connect males of the
same surname. For example if I was able to find another man with the
last name of Miller that is a yDNA match to me, I'd know that we descend
from the same man on our Miller line somewhere along the line.
Family
Finder is Family Tree DNA's name for their autosomal DNA test. Ancestry provides only the autosomal test now. This is
the "everything else" test. This is the bulk of your DNA and can show
connections on any of your ancestral lines, not just purely male or
female lines. This can show connections, as one example, on your
mother's father's father's mother's mother's line and the person that
matches you could connect to you on their mother's mother's father's
father's line, or any other line for that matter. It will tell you that you are related but it will not tell you how you are related. For this, you'll need to narrow down your search by finding common names, common locations, common DNA matches or other ways. This is the challenge!
-- Matt