I have a centre tap transformer 240V – 24V @ 250mA. I know I will get 12V between the centre tap and either of the other connections (I think one will be -12V), but will I have two 12V supplies at 250mA or 125mA? And will the 24V supply be 250mA?
Each half can still supply 250mA. So you 2 12V outputs @250mA.
A common way to use a center tap transformer is to provide postive and negative supplies with 4 diodes.
Be careful about using a bridge rectifier from each half as I see in some circuits, that won't work as some of the diodes short out others.
The total power output depends upon how the transformer was rated but it probably is good for 250mA DC output from each of the positive and negative supplies.