How does the "law of one price" establish a relationship between changes in currency values and inflation rates?
This has to do with purchasing power parity. What the law of one price tells us is that the relationship between two currencies must be proportional to the relationship between a fixed market basket of products in the two countries.
The reason for this is the law of one price. Identical products should cost the same, regardless of the country. If they do not, people will buy things in the cheaper country and bring them home. When they do this, they will be bidding up the prices in the cheaper country (because of increased demand) and they will be lowering prices in their own country (through decreased demand).
Because of this, there will be a relationship between changing currency values and inflation. The currency of Country A will appreciate relative to that of Country B at a rate equal to the difference between the two countries inflation rates. If Country A has 1% inflation and Country B has 3% inflation, Country A's currency must appreciate at the rate of 2% per year.
This has to happen so that the law of one price will hold and the exchange rate will be proportional to the relationship between price levels in the two countries.