Generally, there are 2 sets of segments each with a common anode (or cathode), to reduce the number of connections between the chip and the display. The transformer is center tapped, one side goes to one set of anodes, the other goes to the other anodes. There is a phase detection pin on the chip, it knows to output one part of the display on the fist half of the cycle, then when the mains goes to the next part of the cycle, it displays the next part.
Diode segments A,B,C,D, common anodes are on 1st half of the cycle,
Diode segments E,F,G common anodes are on the 2nd half of the cycle.
Segment A cathode is connected to segment E Cathode, similarly B and F, and C and G.
The clock chip counts the mains cycles, and knows which part of the display to show at each point.
My clock draws about 60mA continuously on bright, about 40-50 on dim. The original transformer was about 5v, I'd be using a single cap and resistor on each output as a voltage doubler on a 3v transformer to provide a current limited output, this would give about 5.3v taking the diode drop into account.