One of the most misunderstood things about martial arts is rank.  Different
people in the martial arts world have different feelings about the use of
ranking in the martial arts.  Some feel it is all important, some that it
is of no import whatsoever, and others that it is a valuable tool not to be
given too much weight outside of its limited context.  What you should know
is that most martial arts have a ranking system but many do not and that
rank within one system does not equate to skill within another system even
though the systems may be similar.  Just because you know how to drive a
car doesn't mean you know how to operate a back hoe.

The most common ranking systems are the Japanese and the Korean systems.

The Japanese systems start with sub-"Black Belt" or Kyu ranks and work from
highest to lowest as skill increases, typically from 10th Kyu up to 1st Kyu
and then "Black Belt" or Dan rankings, from 1st Dan and going up to 9th
Dan.  9th Dan is typically reserved for the (one) highest ranking
instructor of the art, usually in Japan.

The Korean system works much the same way, simply substitute "Gup" for
"Kyu."

You should also know that some Occidental systems have a rank system, but,
when they do, they usually do not follow the 10th-1st sub-black belt then
1st Dan-9th Dan ranking that Asian systems do.  Frequently Occidental
systems will rank a practitioner by number of wins in competition or a
combination of skill level rankings and competition wins.  Savate schools
will typically operate in this manner.  Other Occidental arts use an
archaic ranking system that includes 4 or 5 ranks starting with "Scolaire"
(Scholar) and culminating with "Maestro" (Master).

Be aware that the color of a belt as a rank in one system does not
translate to the same rank in another system.  A "Green Belt" in one system
is usually not the same rank as a "Green Belt" in another system.  The same
goes for Kyu/Gup ranks.  As stated earlier, a Kyu/Gup rank in one system
does not equate to the same skill as an equally numbered Kyu/Gup rank in
another system.  Simply put, you can not compare a 5th Kyu in "Karate" with
a 5th Gup in "Taekwondo" and they probably wear different colored belts. 
At this point, it should go without saying that a "Black Belt" in one
system isn't really comparable with a "Black Belt" in any other system.  It
only represents a certain level of skill obtained within _that_ system;
exactly what skill level that represents is entirely up to the instructors
who define _that_ system.

Again, don't be overly concerned with the rank of the instructor.  You
likely will be unable to differentiate between a 3rd Degree Black Belt and
a 9th Degree Black Belt for many years.  Further, it is held by many in the
martial arts world that you can learn a lesson from anyone, even the
lowliest practitioner.  Learn the lessons that the instructor has to offer. 

A final word of warning on the rank of the instructor.  Beware claims of
inflated or high rank.  It is not unheard of for a martial artist to break
away from his parent organization or instructor and award himself "9th Dan"
and "create" his own art.  More then one instructor has made the leap for
3rd Dan to 9th Dan in this way with no real increase in his skill or
teaching ability.  Further, some organizations have been known to grant
additional rank to instructors for "services to the art" such as opening a
school in an area previously unreached by that art or for some other notable
promotion of the art.  

Beware any school where the instructor seems uneasy about you talking to
the students without the instructor standing right there. It's also not a
good sign if the instructor seems nervous, self-conscious, or hostile,
about you watching him/her teach, or if the students themselves seem
fearful or nervous around the instructor.  Caveat emptor.

Finally, the natural question asked is, "How fast?"  ...How soon will you
get your coveted Black Belt?  How long before you can "defend" yourself? 
How much time before you can kill everyone in your neighborhood without
breaking a sweat?

...We don't know...

Or rather, to be more precise, it depends.  Each statement is a different
goal, though they all seem to be related.  Again, a "Black Belt" means
different things to different martial arts systems.  To some it means
"you've got the basics and are now ready for a little bit of a challenge."
To others, "You are competent in the system enough to be let out without a
chaperone." To others still, "you know enough to be able to defend against
the unskilled or moderately skilled." And to others yet, "you're an
'expert' in the same way that a new trade skill grad is an 'expert' but not
the same as a 20 years experience 'expert'." Remember, "Black Belt" is only
meaningful within the context of the system you're studying.  That being
said, it is not unreasonable to expect that, with modest effort, the
coveted "Black Belt" may be achieved within 4 to 7 years of practice.  Many
systems track, even require minimums of training or "mat" time between
promotions.  It is thought to be more meaningful to talk of the number of hours
spent "on the mat" (ie, training), than to speak of the "number of years."
Simply put, if Dick spends 2 hours a day, twice a week, training to achieve
"Black Belt", and Jane spends 4 hours a day, 5 days a week, then Dick
is going to sweat for five long years to rack up 1040 total hours of
training, but Jane will have done that by the end of her first year.

As to the issue of being able to "defend yourself," that all depends upon
the skill level of the person or persons attacking you, your skill level,
weapons involved, and a myriad of other variables.  The stories of students
with one class under their belts defending themselves are true, likewise
the stories of "Black Belts" being beaten up.  There are just so many
variables involved that the question is near meaningless.  However, the
more diligently you train and the more time you put into your training, the
more likely that, if the unhappy time ever comes, you will be able to
successfully "defend" yourself.