Remove the hub cap. There will be 3 lug nuts holding the wheel on the cont'l kit ass'y. Remove them, and take the wheel and it's fiberglass cover off as a unit, lay them flat on the ground (blanket useful to prevent scratching). There's a spring on the bottom to hold the "donut" closed, remove it. Pull the donut apart until the front flat piece (fiberglass, covers the sidewall of the tire) can be taken out. Then pry the donut apart further, and remove the wheel. It's a complete pain in the @$$. When you're frustrated with this process, but a can of fix a flat and a cell phone, and keep them in your car. If the fix a flat won't do it, call a roadside service company to come help you. This frees up space in your trunk that a jack would take up. Freeing up this space also keeps you from damaging the vehicle with the piece of crap jack that comes with the cars. The other option is to get one of the modern "reduced size" spares, and keep it along with a smaller jack (like the bottle jack from a Jeep) in your trunk.
Any way you slice it, removing the cont'l kit, and then the tire from the kit stinks.