A detailed explanation of BIS' methodology is available here. ZeroHedge explains the results and why the BIS effective exchange rate is a better measure of currencies' relative value than the nominal rates that most campaigning politicians ignorantly use:
It is evidently clear that since 2005 the USA has been on a path of very considerable currency devaluation - down almost 16% while the Yuan has strengthened almost 38% based on the BIS [real] effective exchange rates. The effective exchange rate (EER) provides a better indicator of the macroeconomic effects of exchange rates than any single bilateral rate...The BIS report also explains:
A nominal effective exchange rate (NEER) is an index of some weighted average of bilateral exchange rates. A real effective exchange rate (REER) is the NEER adjusted by some measure of relative prices or costs; changes in the REER thus take into account both nominal exchange rate developments and the inflation differential vis-à-vis trading partners. In both policy and market analysis, EERs serve various purposes: as a measure of international competitiveness, as components of monetary/financial conditions indices, as a gauge of the transmission of external shocks, as an intermediate target for monetary policy or as an operational target. Therefore, accurate measures of EERs are essential for both policymakers and market participants.The chart above shows REER for the Dollar (USD) and the Yuan (CNR). I've emphasized real rates over nominal rates several times myself. In short, the BIS REER attempts to reflect the actual costs of goods and services in different markets, and it achieves this goal far better than the nominal bilateral rates that are constantly regurgitated by angry US politicians. And the BIS REER data for the United States and China (which you can check for yourself on BIS' website) demonstrate a significant Yuan appreciation and Dollar depreciation over the last 6 years.
Funny that you don't hear about that in the campaign ads and TV debates, eh?