I just upgraded my front speakers in my MY10 as you and you need the following: small flat screwdriver with the tip taped up, phillips screwdriver, a plastic putty type knife and a dedicated automotive trim panel remover. All of these could be picked up at your local parts store.
First find the little screw covers in the handle and door. Gently pry them with your covered flat blade screwdriver and remove the screws.
Next find the little slot on the armrest control plastic on the side closer to the front of the car. Hold the same covered flat screwdriver more towards a vertical position and push toward the sky. Levering didnt work for me, I just pushed up and the spring clips gave way. You can then just lift it off and work it around with your hands. You have to disconnect the switch plugs. Remove 2 more screws.
To remover the actuall panel I started toward the rear of the door but Im sure you could start anywhere. I slid in a plastic putty knife to gently pry away so I could find the white clips and then used the trim panel tool to pry the door panel off. work your way around the bottom and sides. The panel will come off but there is the light to disconnect and the door opener cables. Just pop the cables out of their stays and the cable end should slide out of the capture.
Now just pull the whole panel up and it should come off easy. The rears should be the same principle.
putting on is just the reverse.
You will enjoy as I did because the factory audio is HORRIBLE!