This is just a basic overview. The steps listed are general and not specific to any car.
The first step to working on anything attached to the electrical system is to cut the power to the system. So you will disconnect the negative battery cable from the car battery.
After the power is disconnected, you will need to remove the trim panels around your stereo. This is the tricky part that you need to look up for your own vehicle. Hopefully it will only be a matter of pulling off the panel and unscrewing some screws.
Once the panels are free you have to remove any screws holding in your current car stereo. After the screws are out you should be able to pull out the stereo. From there you need to unplug the car antenna cable, the power cable, and the wiring harness.
The wiring harnesses can be different from car to car, so a new stereo may require getting an adaptor to be able to connect to the car. Or if you are adventurous, you can rewire the harness to use with the new stereo.
When you have your needed adaptors or have rewired the harness to your new specifications, it is time to install your new stereo. Reattach the wiring harness, the radio antenna, and the power cable to your new unit. Mount the connected unit back into the dashboard and screw it into place. Replace any mounting hardware for the faceplates and the plates themselves.