The setup itself is fairly straightforward. A decade counter lights each LED up in sequence. There are 5 lights in parallel, so you will see5 lights active at any one moment. A 555 timer sets the clock for the decade counter, and a voltage divider with 1MOhm trimpot allows for speed control. The diagram below gives a rough view of the circuit.

I first built it on a protoboard just to make sure I didn't miss anything obvious in the design. There are 10 lights in the loop.

I lined up all 50 LEDs so the cathode could be bent and soldered in 5 groups around the rectangl, with a 1 KOhm resistor for each string.

At this point in my still young hobby I had done some circuit design and soldering, but not enough to plan it out well. Hence the messy wiring. It wasn't pretty, but got the job done. I managed to keep all but a few wires hidden in the back.

And finally, the complete loop: