What did happen, what could happen and what will happen.
What did happen:
When Greece joined the Euro the government got access to cheap credit. The politicians used the cheap credit to take up public debt. (In other European countries private debt was the problem). The politicians then used the cheap money to buy votes and ignore severe problems, like rent-seeking minorities.
Rent seeking minorities are one of the biggest problem in any society. The problem exists in the US (e.g. sugar regulation) as well as in Germany (e.g. sales tax for flowers is reduced.). The reason such nonsense happens is that a well-organized minority exerts political power to enforce its own interests. The reason this is possible is that the minority is small. For example, the typical US citizen doesn't care all that much that he pays a few dollars the year more for sugar. But the sugar industry cares a hell of a lot because these dollars, added over the entire US, mean millions of $ for them.
In Greece e.g. you can't just open a taxi business. Instead, you need to apply for a license. But the existing taxi drivers don't have an interest in competition. That's why they made an agreement with politicians to vote and support them financially only if the politicians keep the supply of taxi licenses artificially small. Now, there are usually a few good reasons for such licenses. Be it quality of the service or fraud protection for the customers. The taxi driver organization probably lists these advantages when they argue publicly. But fact is that there is no reason for society to keep the pool of licenses small. This only leads to not enough taxis and artificially high prices. These artificially high prices, created by lack of competition, are called a rent. Just like US citizen pay too much money for sugar, the Greek pay too much money when they want to use a taxi.
The taxi drivers are a rent-seeking minority. The problem is that the majority of the citizen doesn't really care about the minority. But in aggregate the minorities can pose a big problem for any society - including the taxi drivers. Greece has many, many, many rent-seeking minorities.
The Greek politicians also employed much more public servants than necessary. From a societal point of view these people are practically unemployed as there's nothing to do for them. Moreover, processes in the public sector are kept deliberately labor-intensive to justify the presence of many public servants. But even though they are practically unemployed - or their work is useless as what they do could be done more efficiently - they receive a generous payment and pension from society.
These public servants need to be fired. It would be good to do it slowly as it can and does financially ruin families. But unfortunately there's no time ..
The Greek government fails to tax their rich citizen. This results in a very high tax burden for the poor and the middle class. This is not just a problem of social justice but really a problem of revenue as the rich by definition have much more money than the rest.
In a way this is also a way of rent-seeking. In this case, those politicians in power had no interest in taxing their financiers more. It's basically the same problem the US is getting itself into right now. Just that in Greece's case the theoretical taxes on the rich are reasonable. There's just no institution which is able to make the rich actually pay.
Finally, evading (value-added) taxes in Greece is considered a trivial offense. The Greece don't like their government because they know it is inefficient. But, in contrast to the US, they still really like to receive benefits from it. And they consider it acceptable to cheat the government. The wider public hasn't understood yet that by cheating the government, society cheats itself. This leads to the honest citizen having to bear a larger burden to make up for the dishonest. It also leads to the dishonest having more money than the honest and thus more influence.
When private external investors gave money to the Greek government and the government to the people, everybody had a lot of money (relative) to spend. This lead to very high prices. The high prices lead to high wages. These wages were so high that the products Greece could produce, were not competitive with the products from other countries outside Greece. And this lead to companies which produced products for consumers in other countries going bankrupt. The workers in these companies found jobs in companies which produced for Greek people. This also lead to Greece importing much more than exporting. But this is only possible as long as the money from the outside flows in. Now that this flow of money has stopped, there's not enough money to buy all the goods from other countries.
More about this further down. The point here is that the people producing goods and services for other Greeks would need to find new jobs in companies that sell goods and services to other countries. But the Greek wages are too high to do this competitively. This problem can only be solved by either reducing wages or by the Greek people (and the organizational structures of their companies), magically, becoming more productive. The latter is not going to happen overnight. That's why wages and thus prices have to go down. Greece needs a deflation. If they had their own currency they could inflate it and achieve the same effect (and a few problems). But now that they are in the Eurozone they can't. Wages need to go down before they can go up again. So, if reporters say that Greece needs growth they are only half-correct. Greece needs a recession to reduce wages and prices today in order to grow tomorrow. This process is very painful, unfortunately.
A few years ago private investors started to doubt that the Greek government will ever be able to pay back the debt. Since then they don't give any more loans. Unfortunately the Greek society, over the last decade, has been transformed to depend on the flow of money from the private investors. Without it there's just not enough money to pay the public servants or really the public sector, which has grown very large. And as the workers in the public sector receive less income, they can spend less on products created by private companies. The result is a severe recession. (Vice versa, this is the reason why increasing public spending does increase GDP - temporarily).
What could happen:
The Eurozone has basically two options.
First it can do nothing. In that case Greece goes bankrupt. And since Greece can't print its own money right now, it had to cut government spending down to what it takes in. This would cause an incredible economic shock. Whole families would starve to death and the population would probably revolt. Some kind of leader would rise to power and start printing a new currency in a chaotic process.
This currency would not be worth very much but it would help. Of course, the rich Greek citizen have transferred their Euros somewhere else a long time ago. Only the less well off and those who don't understand economics would suffer when they try to get their money from their bank, because they would only receive the new currency and not Euros. And the new currency would buy much less goods and services than the Euro.
The magnitude of the problem can be understood best when looking at what Greece imports and what it exports. Imports in 2011 were 43 billion Euros but exports were only 22 billion Euros. Since no one outside of Greece gives Greece any money, the imports would necessarily be reduced to a maximum of about 22 billion Euros overnight.
Since Greece is a very small country, most of what the citizen consume is produced somewhere else in the world. And many of these things are very important nowadays. Take oil, meat, wood or computer chips as an example. To suddenly cut the imports of these things down from 43 to 22 billion Euros would be one, if not the, most extreme shock in modern economic history. The economic recession would rival any in Sub-Saharan Africa over the last hundred years. It's so extreme that its effects would really be completely unpredictable ..
The alternative is the Eurozone giving Greece money. It does so in the form of debt, but we all know that Greece won't repay most of it. In return for the money the Greek politicians are required to reform the country. For example, to deprive rent-seeking minorities of their power. Now, this is causing a hell of a lot of problems for the Greek politicians. They need the rent-seeking minorities to be reelected. But they won't be reelected without the money from the Eurozone. The result are extremely agitated negotiations and a few politicians who think that they'd rather be the prime minister of a failed nation than not being reelected ...
Should the reforms actually succeed to a satisfying degree, which I doubt, the Eurozone might be convinced to actually help with an investment program; a kind of Marshall plan for Greece. Right now, however, would be the wrong time as such a plan would remove pressure from the Greek politicians. But if the government reforms turn out to be convincing, such a plan, in a few years, would be a great help for Greece - and for the European project. The point really is that the Eurozone will only throw more money at Greece if it thinks that it will help long-term. Right now it would help only short-term.
What will happen:
Now, unfortunately the future is bleak. Most citizen don't understand what is happening and they behave perfectly humanly if they try to break out of dire problems by doing anything. For example, by electing some politician who promises to have some simple answers. Germans have some experience with politicians who offer such promises in the time of economic need.. mix in some nationalism, for example, by threatening Turkey and there you go. Greece still spends over twice the percentage of GDP (3.2%) on the military as e.g. Germany (1.4%) - and somehow the Greek politicians rather cut pensions than military spending ...
If you ask me this is what will probably happen. The Eurozone can't give much more credit to Greece because four to five European countries have problems themselves. And the politicians of the countries who don't have problems, most prominently Germany but also Finland, the Netherlands, Luxembourg and Austria, have a really hard time being reelected if they transfer ever more tax payer money to Greece.
Furthermore, the Eurozone public debt crisis, except for Greece, is about to be solved by the ECB (as I predicted) and a little support by reforms in Spain, Italy, Portugal and Ireland. This means that the Eurozone has very good chances now (as opposed to a year ago) to survive Greece leaving the monetary union (no irrational chain reaction). And thus the willingness to transfer money to Greece is dwindling fast.
Thus, if you are a young Greek: get your money out of the country and learn a second language to a degree that you can find work in another country. Because, no matter what happens, Greece will have dire economic problems for at least the next ten years. If everything works perfectly it could then rise again .. but if Greece steps out of the Eurozone, or even the European Union, hope will not return for a long time, ...