OK, now you asking some questions that can be answered ;)
I guess the easiest way to do it would be to add an include file to the top of every page in your site, so you can manage the functionality from one place.
Then add a variable declaration for the exchange rate. If you want you can get it from the database, or just update this file directly to reflect accurate rates.
You can create and set a sesison variable on the included page to keep track of the currency settings. You can apply the "set session value" server behavior in the general section of ecart to set the value of the session variable to "EURO" if it is not defined to accomplish the desired result.
This will then give you the session variable and the exchange rate on any page where you need it. From there you make your "Show prices in" option simply update that session variable.
Then wherever you reference a price "[pricecode]", you can instead reference it:
(($_SESSION['CurrencyFormatSessionName'] == "USD")?([pricecode]*$_currencyRate):[pricecode])
The same general principal would be used whenever displaying currency in the cart or on the page where you need currency conversion.