Essentially this process is just the reverse of installing a dishwasher. Firstly, disconnect the electricity at the nearest circuit breaker, and disconnect the water at the shutoff valve underneath the kitchen sink.
Pull the dishwasher out slowly until it becomes restricted by the power cable or water pipes. It's best to disconnect the electricity first. If the dishwasher is plugged in to a nearby power socket, follow the power cable to the source and unplug it. Thread the cable out to the dishwasher, and pull the dishwasher out further if the power cable was initially restricting it's movement.
If the dishwasher wasn't plugged in to a local power source, you will need to get the screwdriver out. Find the junction box (where the power cable goes into the dishwasher). Unscrew the front panel of the junction box, and you should see the wires inside. Disconnect these wires with your screwdriver. Pull the wires out of the box, and the dishwasher should be free of the power cable.
Next up is the drain outlet. Look in the cupboard underneath the kitchen sink, and find where the drain outlet connects to the sink outlet. Disconnect this, closing off the connector on the sink at the same time, so that water won't leak out. Go back to the dishwasher, and gradually pull the drain outlet piping until it's free. All that should be next is the water inlet pipe.
Find where the water inlet pipe connects to the dishwasher. There should be a 90 degree fitting where it connects. Unscrew the pipe from this. Remove the Teflon tape from the 90 degree piece, so that it is ready to be connected when the new dishwasher comes.
All 3 of those connections should now be disconnected - the dishwasher will now pull free when you move it.
To dispose of your old dishwasher, there may be an option with the delivery of your new dishwasher, to remove your old dishwasher. If not, it's a bit harder work - get some help with the lifting, and take it to your nearest dump, checking first that it's ok to dispose of your dishwasher there.