The cable-basic colouring is;
BROWN: Common ground. This is the rails and trackbed. Also the common ground/return is used for changing signals and points; In that case the brown goes to the blue or white push-button controllers.
All brown connectors should be joined together across all transformers. (Beware of wall-plug orientation; all trafos MUST be in"phase" for doing this!)
RED: Train running power: Goes to the center-strips/pukos of the rails. Powers the sliders of the locos.
Reds must NOT be connected across trafos, and normally a small insulator (i.e. piece of paper) is inserted between the rail-sections where different REDs would otherwise meet.
If there are signals for train-control, one of the red from the signal should be connected to the trafo, and the other to a small insulated section of track.
YELLOW: Constant 16Vac power. Used for lights, like signals and point lanterns. Each bulb consumes approx. 1VA, so lights should be distributed with care. Often a dedicated trafo will be used for lights. In your case you should use the older blue trafo for this purpose only, and NOT for running trains.
Each point and signal (and decoupling track) will have to be connected permanently to a yellow socket. The solenoids in these only consumes when activated form the blue or white control boxes, so is normally not a problem.
BLUE: Control of points and signals (solenoids). The blue cables are connected to the red&green connectors on the blue or white control boxes. (Remember that the blue or white control box is in turn connected to the brown common ground!) These control boxes operates the solenoids by closing the circuit between brown and yellow wires!
Sometimes you will find GREY wires. These can be any kind of the above mentioned. Each case is special.
Most of the blue or white control-boxes are for controlling points and signals. (The boxes with red&green buttons), but there are 2 other kinds, which both are used as permanent on/off switches for track-power (RED cabling) to sidings, or light on/off in houses or other accessories (YELLOW cabling)
That should get you started on the basics... Good luck! ;-)