What is contagion? From the World Bank:

Contagion is the cross-country transmission of shocks or the general cross-country spillover effects.

Basically National Economies are linked through Globalziation and thus when one financial system is affected it spreads to other national systems.

Financial links exist when two economies are connected through the international financial system. One example of financial links is when leveraged institutions face margin calls. When the value of their collateral falls, due to a negative shock in one country, leveraged companies need to increase their reserves. Therefore, they sell part of their valuable holdings on the countries that are still unaffected by the initial shock. This mechanism propagates the shock to other economies. Another example of financial link is when open-end mutual funds foresee future redemptions after there is a shock in one country. Mutual funds need to raise cash and, consequently, they sell assets in third countries.

So does anyone understand how all of these financial systems interact in order to contain and not spread financial crises?

Answer: NO

There are theories, even trying to describe all of this interlocking as herd behavior (like CEO pay?), yet in terms of truly understanding the global system, at least in my diggings, seemingly how all systems interact is simply not understood.

Now the IMF is warning on the global financial crisis:

"Failure to do so could usher in a period in which the ongoing deleveraging process becomes increasingly disorderly and costly for the real economy

The IMF is saying Deleveraging is necessary and inevitable.

A more resilient financial system will ultimately emerge from restructuring and deleveraging, but market forces are in the meantime resulting in a disorderly, accelerated adjustment process, requiring the use of public balance sheets to restore order. In this environment, financial firms face enormous challenges in raising capital to cover losses, while efforts to shed assets are keeping downward pressures on prices. In addition, doubts about the soundness of some banks and their business models have led to severe impairment of the funding markets and sudden and at times unruly consolidation in the sector. Government initiatives aim to support a more orderly deleveraging process, but its difficult and protracted nature is likely to curtail credit availability, placing a further drag on the economic recovery.
The most significant risk remains a worsening of an adverse feedback loop between the financial system and the real economy.

So, does anyone have any idea on how to stop contagion?

In this paper, Contagion: How it spreads and How it can be stopped (2000), the problem is clearly acknowledged, they don't know how contagion works:

The exact causes of this volatility are not yet known nor how to design the best system guiding the movements of international capital, i.e., the “international financial architecture.” Yet, reducing volatility and contagion has been an important stated objective of recent reforms.

Ok, financial wiz folk, what's the answer here?

Further research whether theoretical, empirical and case-studies, or covering the role of international financial agents and the international financial system may shed light on these aspects, thereby help identify characteristics which make countries vulnerable to contagion, and develop specific policy prescriptions to reduce the risks and manage the impact of contagion, and recover as efficiently as possible from the impact. In the meantime, it will be difficult to identity whether any measures beyond strengthening the international financial architecture more generally can reduce the risks of contagion specifically.

Are you kidding me? They have built up this massive global system and have no idea how to contain it, to stop it from spreading when one component fails?

Well, I guess we have the entire world as one big lab rat for financial forensic analysis after the fact. Great!

Another paper, Financial Contagion: What do we Mean? What do we Know? (2003), goes into more definitions and current theories on contagion. Has numerous graphs on incidents from the 1900's with the Asian< Mexican and Russian financial crises.