I am trying to sell my car.  At the moment, I have a lein against it,
and owe about $8,500 to VW Credit.  I am trying to sell it on
the private market, but don't know how it works with the money - will I
have to give the money to VW Credit in order for them to release
the title to me? What is the common way of doing this if I need the
buyer's money to pay off the loan?

Further, I just moved to Pennsyvlania from California (and the car is
still registered in California. It is also registered under both my
name and my brother's name -- he still lives in California), and am
selling the car in Pennsylvania.
With regard to the title (which is a California title) - does this matter? 
How do I officially transfer the CA Title to someone living in Pennsylvania?

Generally, the lien holder has possession of the title.  The buyer of
your car is going to want the title when they buy the car.  So, you
will have to pay off the loan before you can sell it.
Also, the Pennsylvania DMV has recently become more strict about
transferring title.  All parties on the title have to release it.  I
am not sure how it works if one of the people on the title is not
available to sign it over in PA. Your buyer will need you to have it
registered in PA in your name before the title can be transferred in
PA to them.

Nowadays, I think most people find themselves in your situation when
selling a vehicle i.e. they still have a lien on the vehicle.
With the last two vehicles I've sold the person purchasing the vehicle
has made the funds payable to the lien holder and not to us personally
- the lien holder, in your case VW Credit, can reassure the person
buying the vehicle by verifying the lien and making arrangements to
forward the title to them or to their financial institution, whichever
is appropriate. If the person buying the vehicle is financing it their
bank will take care of most of the hassles by dealing directly with VW
Credit.
It is not necessary for you to find the funds to clear the loan
yourself in order to sell the car. Most people buying cars privately
understand this. Many buyers also like to receive a notarized purchase
agreement when they hand you the check to clear your loan.
You may want to check with the Pennsylvania DMV how the process will
work before you put the car on the market - if there are major delays
on the horizon to meet the state requirements you could lose a
potential buyer. In the meantime you could look into your brother
giving you a limited power of attorney to sell the vehicle - check
that this document is accepted by VW Credit and the DMV.
Hope this helps... I've been there!