In short, you are correct, or so it appears.
Prices actually do not rise. Adjust your thinking this way: it is the value of the currency unit that falls. An example is a loaf of bread. Assume that it takes the same resources to produce the loaf but someone decided to charge $2 for it rather than $1. Basically everyone else will also put up their prices because one commodity has gone up in price, but that commodity required no more to produce than before, assuming no labour or tech changes.
What governments do is much the same thing. They print legal tender instruments, notes and coins, and put them in circulation. This is actually a form of legalised fraud that would send you or I to jail, but governments do it all the time. They can do it because currency units do not need to be backed by a Mono-Metallic (Gold or Silver) or Bi-Metallic (Usually Gold AND Silver) Standard where each currency unit is matched by corresponding stores of welth represented by these metals. Most governments have long done away with these standards, "de-monetising" Gold and Silver, and allowing egregious debasement of the currency and removing true stores of wealth such as precious metals from common public use. This serves governments well. The US Federal Reserve no longer has to report publically how much currency has been printed and coined in the Fed. Mint. Most other countries are on the path to a similarly deplorable situation.
There is nowhere near enough gold in the entire world, that has ever been mined, to back every US dollar, let alone all the other currencies, unless old was priced at an inordinate price per Tr.ounce. In excess of $50, 000 per Tr. Oz would be about right, making the gold required for non-bullion purposes to expensive.
The anglofareast website below has articles on this, and the "Millenium Money" video is on there to watch.
Put simply, the US government started removing the Gold Standard in 1913 (The Federal Reserve Act of 1913 started this), though there had been several "cycles of currency" since America was founded, as there has been throughout history elsewhere.
Hope this helps. Check out the resources: they are easy to dowload or play on screen.
"Millenium Money" Australia Fair Publishing.
Daniels, P. "Destiny" Dan El publishing
Daniels, G "Taxation: from the divine to the ridiculous"
Daniels, G "Why Silver and Gold?"
Judge, P. "Stories from the desk of a Bullion Banker"
Sanders, P. "The Silver Bonanza"
GATA records: GATA Conference 2006.
Martenson, Chris "The End of Money"