1st off I would recommend doing the install with a half tank or less of gas but it's not mandatory.
Next you should relieve fuel pressure. The proper way to do this according to the Mazda shop manual is 1. start engine 2. disconnect the circuit opening relay 3. after engine stalls, turn off the ignition 4. reconnect the circuit opening relay.
I didn't bother doing all this although it's the smartest and safest way to do it. I simply unscrewed the gas cap and dealt with any left over fuel pressure as I went along. If you do not know where to locate the fuel pump circuit opening relay look at this pic provided by magik8.
I hope he does not mind my linking to it.
Obviously you now need to disconnect the battery completely. In fact it's probably a good idea to remove the battery from the car entirely just to be safe.
OK, with the prep work out of the way you should remove the back seat cushion. This is very simple! Pull the carpet out a bit from under the cushion and lift the cushion up gently. You should find two little white clips, one on the right side and one on the left side. Push the clips in and the seat should come up with ease. I apologize for the poor quality but when you get this far it should look like this: