Controlling Transformer Output
It is not clear from your question whether you want a controllable 0-24V AC or a 0-24V DC. You will need to answer to that in order to get much further input. 

If you want DC then you will want to rectify the output of the transformer and build a variable DC voltage regulator. A linear regulator is possible bit it can get really hot when operating at full load current at the lowest voltages. A better solution would be a switchmode regulator.

If you want AC then your solution may very well be a device called a Variac. These are basically a variable transformer. Google to find further details.