There are a couple versions of this project around, this one is my original circuit and code. It uses an ATtiny84A and an MCP79412 RTC. Once per second, the code generates a random number. If it's an odd number, it advances the clock. If it's even, it adds one to a counter. When the next odd number is generated, the clock is advanced by the number of seconds indicated by the counter. The MCU sleeps between interrupts from the RTC, and I calibrated the RTC against a GPS time base. So I hope it will run quite a while on two AA cells, and will also keep good time, hopefully to a few ppm.
I only ruined one clock learning how to hack it. Basically I just cut the traces between the clock motor coil and the original clock circuit, solder a couple wires to the coil and bring them out to my circuit. This particular clock isn't terribly well constructed (which is what I would expect for a $4 SprawlMart clock) and I ended up breaking a plastic bracket in the mechanism. Basically the entire mechanism needs to be disassembled to get at the circuit board. It has five or six gears and is not really too bad once you figure it out.
Here are a couple photos of the board.