A depositary bank holds the ordinary shares abroad and issues receipts against them. Sponsored programs are set up by the company and can list on an exchange; unsponsored programs are created by banks and trade on otc-markets. The receipt's economics track the underlying shares adjusted by the adr-ratio and the exchange rate.
Two frictions are specific to the wrapper: the depositary deducts an adr-fee, and dividends arrive after foreign withholding tax and currency conversion, so the realised yield is lower than the local one.
Example: an ADR represents 2 ordinary shares. The ordinary trades at 40 euro and the euro is worth $1.08. Fair value of the ADR is 2 x 40 x 1.08 = $86.40, before any fee.
Related: adr-ratio, adr-fee, gdr, foreign-ordinary-shares, cross-listing