How does the collector emitter relationship work with a transistor?

An analogy may help to visualize this:

Think of the transistor as a valve or faucet. The base is the knob, the water tends to flow from the positive side (storage tank) to the ground (drain), if you follow the normal "current flow" directions.

The LED is like a little transparent glass section in the pipe, with a small ball loosely held in that section.

When the faucet is opened, water will be allowed to flow, and the little ball will jump around due to the water's flow.

This will happen whether the LED is above or below the faucet section.

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Now for the case of electron flow, as opposed to conventional current flow direction.

Consider the same pipe and faucet, but with the ground being a source for some gas, say natural gas at high pressure underground.

The Vcc is the open air, normal barometric pressure.

Again, as the faucet is opened up, the gas will flow up the pipe, the little ball will bobble around. Again, the glass pipe section (LED) could be before or after the faucet, it won't matter.

I hope this analogy helped.

But, why is the emitter running to ground? Shouldn't it be the other way, collecting and emitting to the LED?

It is, but the charge carriers are negative electrons, so they move (well, nudge each other along, really) in the opposite direction from what the idea of conventional current leads you to expect.