Can someone please tell me how to install a transfomer to a central air unit just to make sure I'm doing it right.because when I put the thermostat on heat mode the furnace comes on and the heat works but every time I call for cool nothing comes on then the tranformer starts smoking can some one please explain by detail thanks.

You have a direct short somewhere in the low voltage lines, so the procedure for finding a short is to start disconnecting things until there is no longer a short indicated.

You can do this test with a box full of fuses and transformers or you can use an ohm meter.

If you have a circuit board you will have two wires coming off the transformer that are the primary side and two that are the secondary side, one primary wire will go to Primary one and the other to Primary two. The low voltage will go to secondary one and secondary two.

What color wires are connected to which terminals on your thermostat? Can you map out which wires go to your air handler or A/C? And is this straight A/C or a heat pump?

Can someone tell me what's the proper color of the 24 volt lines on a transformer and the colors of the 208 volts plus the color to the 240 side

Is possible you have a shorted out contactor in the condenser unit

can someone tell me whats the proper color of the 24 volt lines on a transformer and the colors of the 208 volts plus the color to the 240 side

Look for a cubed shaped object with white common/neutral and red/black hot for input to the 110VAC side, with similar colors on the 24VAC output side. Google for 24 volt transformers to get an idea of what you're looking for. There is likely a label on the transformer that is a dead giveaway saying input is 110VAC and output 24VAC. If it still has power it will be humming and a little warm to the touch, unless you did indeed short it out.