The first noble truth is - Life is suffering. Does it mean Buddha was preaching pessimism and telling every one life is not worth living because it is full of suffering?!? In my experience - nope - that is not what he was saying at all. What he is asking us to do is to analyze what is the so called happiness after which we run so vehemently? We chase happiness so fervently without ever stopping and thinking about its definition and characteristics.
We think of suffering as mental, physical, emotional or financial suffering - times when we are crying out of pain. Other times are either happy times because our ego is getting what it needs to feel good or they are neutral times - times when we don' care. And to us - life is a mixture of these three kinds of experience. However, the suffering when we are crying out of pain is the extreme form of suffering, one we cannot avoid. We endure the unhappy and sad times in hopes that good times will come again and that is what keeps us going.
Now, lets see what Buddha said about suffering --
"Birth is suffering, ageing is suffering, decay is suffering, death is suffering, sorrow, lamentation, pain, sadness, and discontent are suffering, being joined with any disliked is suffering, being separated from any liked is suffering, not getting what one wants is suffering, & getting what one not wants is suffering.." (http://what-buddha-said.net/drops/II/The_1st_Noble_Truth_on_Suffering.htm)
Lets analyze this a bit - see the pattern - anything we "don't" want is suffering. This is also the reason why your suffering is different from my suffering because our wants are different. It is not just anything we don't want, it is also the feeling that comes when we want something, get it and then we are bored of it!!! Now, we want something else. In effect, the happiness that you get by getting something leads to suffering again because either eventually you get bored of it or the thing gets destroyed for one or the other reason. This constant dissatisfaction is what is suffering. It is a subtle form of suffering, not so extreme and obvious which will make us cry, but it is always there, pricking like a thorn, like never quenching thirst - no matter how much water you drink.
When you sit zazen, you become witness to this dissatisfaction. You see for the first time if suffering is driving you or you are driving it. You see how your happiness almost always depends on gaining something, achieving wealth, fame, power, recognition, approval from others etc. Sitting zazen does not give you any magic pill to convert suffering to happiness nor does it result into some kind of "high" that makes you immune to pain. What it does is that it gives you a tool to analyze your definition of happiness and suffering. Hopefully, sooner or later, your definition will change, chase will stop and it will bring peace and contentment which results in true happiness (as per my definition of happiness, yours might be different..:)). It allows you to see the futility of running after impermanent things and renounce both extremes - getting and loosing.