Suppose that Alice buys a house from Bob for a price of 200 troy ounces of gold (which is about average for the present-day US), and assume that she is able to make a single lump-sum payment. There are several ways that this could be done.
Physical gold
The weight (13.71 lb, 6.22 kg) and volume (19.7 in³, 322 cm³, less than a standard soft drink can) of the gold could plausibly fit in a handbag or backpack. Gold is a nicely compact way to store monetary value, and it would require a huge purchase before the logistics of transporting it become seriously difficult.
Still, Alice might not feel comfortable walking through town with a bag full of gold, so let's consider other options.
Paper money (backed by gold)
The United States issued gold certificates from 1865 to 1933, with the Treasury responsible for physically storing the gold. Denominations as high as \$10,000 (500 oz) were put into circulation, specifically to allow banks and the federal government to settle large transactions. The notes were “as good as gold”, since anyone could redeem the certificates for physical gold coins whenever they wanted to.
Banknotes were technically an option before the Civil War, but a much less convenient one, because they were issued by individual private-sector banks. Merchants relied on bank note reporters to help determine whether to accept a particular bank's notes, based on the frequency at which that bank's notes were counterfeited, and the financial solvency of the bank.
Personal check, and the banking system
Alternatively, Alice could write a check to Bob. If the two happen to have accounts at the same local bank, then the transfer of gold/money ownership is a simple matter of bookkeeping. If not, then Bob's bank would have to send the check back to Alice's bank for payment. Since we're assuming a pre-1933 banking system with no modern electronic conveniences, this means physically mailing the check. And Alice's bank would then have to send the money to Bob's bank. And then we're back to our original problem of how to transport the money, except that now it's between banks instead of individuals.
Fortunately, there are a couple of shortcuts that can be used. One is that if Bob's bank happens to have customers that need to pay money to Alice's bank, then the payments will cancel out; only the net imbalance of payments between the two banks needs to be settled.
Also, it's possible for two banks to have accounts at a third bank, called a correspondent bank. In this case, the transfer becomes a simple internal bookkeeping matter at the correspondent bank, with no physical transport of gold. If you expand the correspondent bank hierarchy to the point where every bank in the country is served (directly or indirectly) by a single “bank of banks”, then you get what's called a central bank. In the United States, the Federal Reserve System has served as the national central bank since 1913, though earlier attempts at central banking had been tried.
But in times with a more decentralized banking system, such as the 1837-1862 “free banking” era with no national central bank, no unified paper currency, and no banking across state lines — shipments of physical gold between banks were indeed needed more often. In this era, which coincided with the great western expansion of the US (annexation of Texas, Mexican-American War, Oregon Trail, California Gold Rush), gold would routinely be shipped between banks on stagecoaches. And people would attempt to rob these stagecoaches, thus giving something for Hollywood Westerns to portray a century later.
