In a sense, modern economies (particularly banking and stock markets) are always based on faith. Once people lose faith that, for example, the bank has the ability to pay out, or that the company will remain solvent, then it becomes a self-fulfilling prophecy.
I don't know how much economics you know, so forgive me if this is coals/newcastle, but if not much you might find the articles on fractional reserve banking, Keynes description of the stock market 'beauty contest' and fiat currency interesting.
In terms of where the problem started, it is complicated and quite hard to summarise, but basically IMO the bottom line was the housing market bubble in many countries (US, UK, Spain in particular) and associated consumer lending boom. The interlinking of banks then meant that defaults in one country affected banks in most other countries because they also owned the bad debts.
The Euro makes things worse, because it restricts the things that member countries can do to deal with economic problems.
The basic 'toolkit' that the government has to manage the economy are:
Monetary policy - Interest rates / Currency value (linked to interest rates - all other things being equal, if your interest rate is low, people won't want to hold your currency and its value will fall) / money supply
Fiscal policy - ie taxes / public spending
Once locked into the Euro, the member countries could no longer set interest rates independently. Germany has a strong economy, and values low inflation very highly. When, for example, the Spanish economy slowed, the Spanish govt were not able to do what would in normal times be expected - lower interest rates, let the currency fall, and if necessary live with a bit more inflation.
I'm hoping all this makes sense, its very hard to explain coherently and briefly with a very small box to type in!