How does the money supply grow in the long term? For inflation to happen at roughly 2%/yr and for people to trade the same (or higher) volumes of goods, people must be trading more money. For such a trend to exist in the long term, there must be more actual units of currency that exist (right?) which means actual currency must be being created by the central bank (right?). When does the central bank create this money (or am I wrong in inferring the central bank must be creating cash...)?
Central banks often do not create cash.  For example, in the United States, it is the Treasury department that prints cash.  

What a central bank does most often that has the effect of creating money is to engage in open market operations.  In an open market operation, it does one of two things:  


Sell an asset that it is holding, usually a government bond.  
Buy an asset, again usually a government bond.  


If it sells, it takes money out of circulation.  Obviously it does this less often, as overall the money supply is growing.  More often, it buys.  This transfers money from its account to someone else's account.  Most of the time, this is a purely electronic transaction.  While the central bank may track its account balance, there's nothing keeping it from being negative.  As it grows more negative, we call this money creation.  But again, this is an electronic transaction.  No actual cash needs to change hands.  

Now, someone may go to the bank and ask for the money.  The bank hands that person cash, which it has to replenish.  The bank may ask the central bank to ship it some actual cash.  If the central bank had none, it would have to go to whomever prints the money to get some.  

Because of the way that fractional reserve banking works, most money is actually created by the banks.  The way this works is that someone deposits money in the bank.  Let's say it's \$10 and the reserve fraction is 10% (as in the US).  The bank keeps \$1 or deposits it with the central bank as a reserve.  The other \$9 it can loan out to someone else.  That entity either spends it or banks it.  If it spends, then someone else faces the same decision.  Eventually all of that \$9 is deposited.  

In the new deposit, the bank (which may be a different bank or the same one) has to reserve \$.90 but can loan out the remaining \$8.10.  But now we have two deposits of the same money.  So there's \$19 of deposits with only \$10 of money.  \$9 was created by the banks.  The process repeats until there is \$10 of reserve and \$90 more (10% reserve fraction).  So for every \$10 created by the central bank, regular banks can create up to \$90 more.  

Most of this money will never be exchanged as cash.  People will write checks or use credit cards.  The money will never exist physically.  It only exists as accounting transactions.  

It's not even necessary to involve banks.  Let's say I sell you something for \$10.  But you tell me that you have no cash.  I loan you the money implicitly by allowing you to take the item.  I've implicitly created \$10 of money.  When you pay off the loan, you are implicitly destroying that \$10 by closing the loan.  

In summary, central banks often don't print any cash.  But regardless of who prints cash, most money in the money supply is never printed.  Most money only ever exists as accounting transactions, and most money is generally created by regular banks rather than the central bank.