Assume that the United States decided to hold more yuan in the federal reserve. Which processes does that involve? I assume there is some sort of electronic exchange between the two central banks where dollars are exchanged for yuan. What happens physically? I assume that the Fed will only need to hold a portion (say, 10%) of the reserves as currency, and the other 90% will be just based on the credibility of the bank. Does that mean that the currency worth 10% of the exchange needs to be loaded in a special plane and flown from China to the US and vice versa? How often do those sorts of plane trips happen?
Typically foreign reserves will just be assets denominated in a foreign currency, most importantly government debt. Another popular reserve asset are IMF special drawing rights, which are convertible into currencies of member countries. I don't think there is any amount of physical cash currency in international reserves. You can see the makeup of US reserves here: https://www.treasury.gov/resource-center/data-chart-center/IR-Position/Pages/12302016.aspx
If the US treasury would decide to increase it's Yuan holdings, it will just buy bonds that pay are traded and denominated in Yuan.