Krellin's advice isnt that bad streephie, but let me tweak his answers a little.
With investing, you essentially want your money to grow faster than inflation. Depending upon how risk averse you are, there are several options. But I'm going to go with your 10,000 euro assumption. First off, I would keep 4,000 of it in a savings or checking account, to cover rent and necessities for a few months in case you lose your source of income. That is your most liquid asset.
Now for the rest, diversification is the key - both across asset classes and within them. If you're being really risk averse, go for an inflation adjusted government bond. This pays out at the rate of inflation plus a small real return. However, since inflation is expected to be so low, regular bonds are probably a better choice. I would put 1,000 in a AAA corporate bond, and 1,500 in government bonds.
The other 3,500 goes into the stock market. As krellin said, market indexes are a good way to go. I would put money in a Nikkei index fund at the moment, and a s&p index. The index funds give you diversification across sectors, and having a couple gives you diversification across countries