no-one has ever actually explained this to me, theres stuff on the news here about how much the pound is worth v the Euro or Dollar and stuff, but how do they know or decide that?

is it just done at random or what?

How is the price of everything else determined? (in theory)

Supply and demand.

If demand for the pound falls (less people wanting to buy exports, for example), or the supply of pounds increase (money being printed - quantitative easing), then the pound will fall in value.

Well, that's the basics, there are other factors, too.

Ultimately, it comes down to the inflationary policies of a nation, purchasing power parity and investments into a country.

It is far from a random event, and is a major part of fiat currencies.

Hopefully I can explain it best this way:

The value of one currency versus another takes into consideration what goods and services cost in a country, for its native currency. If the policies of a government are poor, then there are chances that PPP and inflation will become different in respect to other countries' fiat currency.

Ultimately, it comes down to currency transactions between countries. If investors and trade transactions believe that a countries' currency is becoming less worthwhile (due to the printing of more money, or more restrictive rules and regulations on business investments), then the amount of money traded will drop, and the currency will become of less worth.

So in the case of the USD against the EUR, most currency investors believe that the worth of the US dollar (as an extension of inflation and business policies) are going to weaken versus the Eurozone, so they sell off the currency, and buy Euros. That causes swings in the worth of the currency.