I need to find out what happened during and after a foreclosure in
Seminole County, FL.  How can I find out how much the bank sold the
property for, and whether it paid of the mortgage or there was a
balance?  If there was a balance, would there be a judgement against
me?  If they sold it for more than the balance of the mortgage, would
they owe me money?

Obviously I have not posted specific information about the property or
bank.  If that's necessary, I can.  But I am basically trying to
figure out how I can find the answers to these questions.  I have
tried searching for the property on the Seminole County tax
appraiser's website and title search, but there is no entry for the
property.  Also, general information about how these things usually
work would be useful.

This foreclosure was three years ago and I don't have much information
from that time other than the address, the bank's name, and of course
my personal information.

I am surprised that you could find no entry for the property.
Is this where you tried?
http://www.seminoletax.org/RealEstateTaxesInfo.htm

Well, I had tried that site, but I guess I didn't look hard enough
before.  I have now found the record.  It shows how much I paid, then
there's another entry for $100, and then it was sold for about $10,000
more than what I owed on it at the time of the foreclosure.

I wonder what happens to that $10,000?  Was it enough to pay for the
costs associated with the foreclosure process?  Do I still owe
somebody some money?  Do they owe me something (unlikely, I know)? 
These questions are not answered by the tax search.

glad you found it.  I am no expert, but I expect that the bank bought
it for the amount of its total claims: mortgage, accrued back interest
and foreclosure expenses.

From the information you supplied it sounds like the property went
back to the bank at the auction and then they sold it. There is a
court file with all the information, the fact that it is 3 years old
the file might have been destroyed by now. If not it will be available
to view at the county courthouse. There should be a copy of the bid
sheet from the auction to show who bought the property and for how
much. If the property was sold for more than was owed the surplus goes
to pay any additional lien holders against the property. If there are
no additional lien holders the surplus belongs to the homeowner. If
the property sold for less than was owed the lender has the option to
get a defiency judgment against the homeowner.