Before arriving in a distant land, one should check out the way the currency usually trades, using a website such as XE and maybe by downloading a currency exchange rate program such as a mobile currency converter from Oanda.  These can be great tools, but in addition, one should do two simple things.

Figure out currency conversions for basic amounts:  $1, $5, $10, $25, $50, and $100.  Once these basic conversions are memorized, one can then easily estimate most values in one's native currency.  The conversion does not need to be exact: it doesn't matter that $5 is exactly €3.88, just remember that it's about €4.  If one is really great with math, it makes even more sense to just remember a basic multiplier: the price in Euros times 1.25 is about the price in dollars.

In the official language of the foreign land, that is.  Learn all the numbers one can remember and then practice them.  Count, listen to native speakers, and listen carefully.  If one doesn't have a lot of experience with foreign languages, this can be a very difficult skill to pick up, but it's so helpful that it should not be neglected.  And it may not come easily.  The words for numbers are so commonly used that they are almost always spoken quickly and slurred together.  Indeed, think of how frequent it is for "fifteen" and "fifty" to be confused in spoken English and imagine how difficult it must be for one who barely speaks the language.

If any of you readers have additional tips for dealing with foreign currencies, please share them in the comments!