Don't be fooled.
When buddhists talk about seeing things for what they really are (as they are wont to do), they do not mean anything the pesky nonbuddhists might imagine. Such as, seeing the sunrise in all its glory, or seeing the beautiful woman in the street as a real person instead of a sex object (hey, it's summer, guys, I'm just as horny as you!).
The phrase means to see things as impermanent, unsatisfactory, and void of self. These are called the Three Marks of Existence. They are directly connected with the Four Noble Truths and are fundamental axioms of the buddhist philosophy.
You may or may not subscribe to this worldview. Fine if you do. Fine if you don't.
I urge you to remember that this is a religious doctrine. Every valuable spiritual experience in buddhism is supposed to confirm it. If you come out of a meditation session with the revelation that things are permanent and very satisfactory indeed, you'll probably be escorted, very gently, out of the sangha. Or at least seen as a very odd kind of buddhist.
This ties into what I said earlier about Experience and Religion. The truth is, there is no way of directly experiencing all things as afflicted with the Three Marks. You simply don't have the experience of all things.
The Anicca part is the least problematic of the three. We all seem to experience that things start end end. Meditation makes it very apparent that this is the case for our emotions and thoughts, and it does so in a highly productive way. But if you jump from this experience, as universal as it seems to be, to a global assertion about everything in all possible universes, you're committing a fallacy of induction. All you can really say is that it is true, with very high probability, of everything you will ever experience.
Anatta suffers from the same problem, but on top of that, it is rather hard to define what a self really is, and whether this is not just a repetition of Anicca from another perspective.
Dukkha is a different beast. It doesn't fit in with the other two. Anicca and Anatta are ontological axioms, whereas dukkha has an element of psychology to it. Lumping it together with the other two seems inconsistent. It has little to do with "how things really are", and more with "how I relate to things".
In conclusion, I believe that buddhism asks you to take a few key assertions on blind faith, and then reassert them with every "experience" that you have. Buddhists do not experience the Three Marks, but they take them for granted, and then use this framework to interpret their experiences. The experience itself, I maintain, is anonymous. It might be better if we tried not to interpret it at all.
It is a religion. Don't be fooled.