I got home from a short ride up the street today where there was a lot of clicking and skipping of chain links and when I got home I realized my chain had a ton of slack. After looking around on the internet, I tried moving the rear wheel back, but there's more slack in the chain than there is room to move the rear wheel back, so I'm stuck.
A cursory understanding of bikes and reading the internet suggests that it could be a stretched out chain or an issue with the derailleur. This is an old steel 12-speed Raleigh. Granted, I don't take the best care of it (not sure where I'm supposed to wash it and store it - I live in a small apartment), but I do depend on it.
Here's the picture of the state of things: