Assigning dollar values to use values is relatively straightforward. You can, for example, simply assess the price received for resources extracted or the cost of enjoying a resource (including travel costs, not just admission fees). A little ingenuity may be required to calculate use values in some cases, but in principle all of the components of use values have values set by a (relatively) efficient marker and so are a good index of their utility.
Assigning dollar values to non-use values is more difficult, precisely because there isn't a market that we can use for reference. Sometimes creative people find ways to create markets, like the Iowa Electronic Markets (http://www.biz.uiowa.edu/iem/) where you can buy futures on things like what policies the Federal Reserve will adopt or (my favorite in Presidential election years) who will win Presidential nominations of the major party and the general election. But typically those markets don't exist, so economists use a different approach. They estimate what is known as ``willingness to pay'' or ``willingness to accept.''