When a Central Bank decides to increase its gold reserves, where does it get the money to pay for the gold from? How does this vary between countries with different strengths / policies on their currency e.g. US vs Romania vs Egypt?
When central banks buy gold, they use their reserves (their assets).
A central bank's assets are predominantly government bonds, but gold is also part of the reserves (and so is US currency). So, generally, they just exchange one kind of asset for another (gold). How would that work?
Assuming the central bank wants to buy gold on the global market. To do that it needs US Dollars, because that's the currency in which it is prices. Central banks usually have large holdings of US currency (as part of their reserves). So they can simply use these directly, transferring US Dollars into the vendor's account in exchange for the gold.
In case the central bank does not want to lower their Dollar holdings, they need to sell another asset. For example, they could sell a government bond they hold, and exchange the cash they get in return into US Dollars and then use these Dollars to buy gold.