Choosing the correct transformer for the dual rail Welleman regulator kit 8042
The short answer is a pretty good choice is the value of voltage you want at the output. So in this case a 12-0-12 or 15-0-15 secondary. It might also be labeled '24V CT' (for 24 volts center-tapped) or 30 V CT respectively.

The peak voltage produced by the transformer is above the nominal value by a factor of 1.4. You can look up 'RMS' if you want to understand this better. So a 12 V secondary will actually produce almost 17 V peak. That's good, because a few volts are dropped across the rectifier diodes and the so-called "drop-out" voltage of the linear regulator (LM317/LM337 in this case).

The "voltage you want at the output" isn't a good rule for the general case, it just happens to work out fairly well at 12-15 V. If you were looking for 5 V or 30 V out you'd want to take a sharper pencil to it.

Line transformers come in two varieties that will work here. One is a "dual secondary" and the other is "center-tapped". A dual secondary has two completely separate secondary windings, meaning four separate wiring connections there. A center-tapped will usually only have three. Either will work in this case since there is just the one "0V" connection to the transformer.