Say two photons start at point A, and go in opposite directions. They will be traveling apart at 2x the speed of light correct? So if this limit is how fast you are able to travel through space (and ignoring the expansion of space itself) is there a way to tell how fast we are moving through space and which direction? Such as measuring in every direction how fast a photon is traveling, and the speed of a photon would be the speed of light +/- our speed. If it's possible I assume it was done and we can know which way we are "drifting" through space? I feel I probably just don't understand something about how the speed works, but that's why I'm asking this question.
According to Galilean relativity, velocities $u$ and $v$ add according to
But relativistically, the relationship is not straight addition, it's
where the units are such that $c=1$. If you put in $v=\pm 1$ in this equation, you get a result that is just $\pm 1$ again. So in your experiment, you will always measure all the photons to have velocities equal to $c$, and you won't get any information about your own state of motion.
Ben's answer is technically correct, the best kind of correct, but I'd still like to expand on it a bit...
They will be traveling apart at 2x the speed of light correct?
No. In fact, this is the entire basis of relativity.
What you're doing is basically adding the speeds. You could think of two balls on a desktop and you have a ruler and you measure them as they move apart. Now you just replace that with light, its the same thing, right?
This sort of thinking has an inherent underlying assumption that you don't even notice. It assumes that measurements lie outside space. To illustrate, imagine an infinite 3D grid of points in space. You probably had no problem doing that, right? But think about it... what you just did cannot possibly physically exist in this universe. Yet it's precisely that sort of imaginary construct that you're measuring against, you simply construct "a space" with certain properties, like an imaginary point every inch, and you're basing your measurements against that underlying construct.
But what if that's just not right? What if the measurements you're taking can't be based on some imaginary grid? Is this really that surprising, considering your ruler is a physical object in this universe? If an infinite 3D grid is not possible within the universe, how can you base anything on measuring against it?
What Einstein (and many others) demonstrated is that if you stop thinking about measurements being these purely theoretical concepts, and instead part of the system, you can't talk about the measurement you're making. Think about it, how exactly would you measure the speed of two photons going in opposite directions if you can't go faster than the speed of light? You can do that measurement in imaginary pure-number world, but not here in the real one.
And that's where the formula that Ben posted comes in. If measurements cannot be based on absolute numbers, they, inherently, have to be relative to the measurer (you). And when you factor that in, then the maximum speed you can ever see is c.
So that brings us to your original question...
is there a way to tell which direction we are moving through space and how fast?
In spite of everything I said above, yes, you can. But that's because of something entirely different.
Space is filled with photons left over from the big bang, we call it the cosmic background. It's everywhere. Now although you always measure the speed of light as c, its energy when it hits you may be doppler shifted in the same way an ambulance siren is when it drives past. So if you measure the energy, which we see as color, of these photons and average everything, you'll end up with a clear asymmetry in their speeds - one side of the sky is bluer and the other reder. Presto, there's your speed. And, IIRC, the Milky Way is going about 0.01 c.
Now if you make the question more theoretical, could we measure our speed in some other universe with no background, well then, no. There is no way to measure your speed without reference to something else. Again, that's the whole idea of relativity.