How should the chain be routed on this deraillier? I feel dumb asking this, but how should the chain be routed around the cogs on this deraillier?

I had to split the chain and then put it back on. I didn't pay attention to how it went round. This is not the right way (below) as the chain is extremely slack.
You almost made it...   Obviously bottom long line should run straight to crankset.  You will feel some spring tension when you route the chain.