I know that this might be common but I just got interested in philosophy...
It is indeed a common question, at least in the sense that almost everyone has considered it at some point in life. And yet, as common as it is, it leads directly to some of the most difficult, profound ideas. As Strawson once wrote, there is no shallow end in the philosophical pool. So, it needn't bother us that the question is a common one. However, the question is also a HUGE one, as philosophers have had many, many different ideas about it. I can't possibly summarize all of it here (not that I know all of it!). But I can offer a few different ideas about what direction one might take in thinking about this question.
One idea is that we can somehow tell, given the content and character of our current experiences, that we are awake. Dreams, according to this idea, are seldom if ever this coherent, this consistent, and this integrated with our accessible memories. And experiences in dreams are never this "stable" or lucid. So, we have empirical evidence, or evidence based on our present experience, that we are not now dreaming. One problem with this idea is that we've been convinced before that we are awake and then discover that we were dreaming. And as correct as the idea sounds to us right now, the impression that we were awake during previous dreams have also convinced us of their "correctness." But, perhaps more troubling, we might ask: how do we know that this isn't a dream unlike any we've had before, in that it is more vivid and apparently coherent than any other dream we remember?
Another, second idea in response to the question is that the what we mean by terms like "table," "chair," "body," and even "dreaming" are just whatever we are actually confronted with at this moment. It would follow (though it takes lots more theorizing to get there) that I cannot possibly mean something true by "I am now dreaming" or "this apparent table in front of me is dreamed, and not a real table." However, one may well doubt that this theory of meaning (not that I've given it its most subtle, effective formulation) is true. Couldn't you truly assert, while dreaming, that you are dreaming? Isn't this what sometimes happens when you have a lucid dream (a well-documented phenomenon)? Furthermore, and perhaps more telling, this response to the question doesn't seem to satisfy us even if we grant it is correct. Even if we grant that whatever we mean by "I am dreaming" is false, all this seems to show is that we cannot formulate some troubling hypothesis. That is, we seem to be able to describe a possible situation in which reality is not as it currently seems (notice I didn't exactly use the term 'dream'), and we apparently can't rule that out, even if we can't use our ordinary terms to express the possibility. We are left with a feeling that something inexpressible could be true, and if it were true, reality would be disturbingly disconnected from how things seem to us.
A third way to answer to the question is to suggest that, though it might be the case that I am now dreaming, the best, or simplest explanation of my present experiences is that I am awake. This may sound like the first response, and in some ways it is. But it adds a crucial element: explanatory considerations. By thinking about my experiences and the way they are now unfolding, I conclude--according to this idea anyway--that the simplest explanation for them is that I am now awake. In the first idea, I read my awakeness, as it were, directly off of my experiences. So, does this explanatory addition help? It might, but it all depends on how the many details are filled in. I don't know how to fill all of those details in, and even if I did, it'd be a very long story. We'd need to specify in what sense, exactly, is the awakeness explanation better, or simpler, and why it is that, in this instance, the simpler explanation is the more likely, or rational, one. And, I noticed you asked how we "really know" whether we are awake. Does noticing that an hypothesis is the simplest explanation suffice for KNOWING that that explanation is true? REALLY KNOWING? These are some pretty controversial questions, but anyway that's one direction to explore.
Let me suggest a final sort of reply to you question: we cannot really know whether we are dreaming or awake. This is the "skeptical" reply. From here, things could go in various directions. You might think that therefore you don't know anything at all about the world around you! After all, if you don't know that you're not dreaming, how could you know that there is a table, a poodle, and a computer in your room (as there seems to be, let us suppose)? But you might question that. You might think that, even if you don't know the very large-scale claim that you are not dreaming, you still somehow know that there is a table in front of you. In fact, this is one way to use some of the insights of the second reply, above, in a more skeptical spirit. Tables, for example, are just whatever THIS is (point to the apparent table). But who knows if this is all a dream or not? Another direction to go is to think that you don't know whether you are dreaming this, but that's just because you never really know anything at all. This is just a particular instance of not knowing, or ignorance, which is everywhere. Sure, I don't know whether I'm dreaming. But I don't really know anything, so that's not big news. Knowledge is an impossible standard.
What a strange situation we find ourselves in! It is such a remarkable and yet, as you say, "common" and perhaps obvious thought that this might all be a dream. And it's not at all obvious how we could know whether that is the case. Is this bad news? That's another, related question. Does it matter? Here's a thought: if this is a dream, it doesn't matter whether this is a dream. So it couldn't be a dream while it matters whether it is a dream. I'm not sure that's right, but it can be a tempting thought.
As you can see, there's just so much to say. Great question! As Descartes once observed, consideration of whether you are dreaming makes you feel a little dazed, which makes it seem all the more plausible that you are in fact dreaming. Just don't try this while driving or operating other heavy machinery.