Newer wine bottles sometimes come with a plastic cork. Plastic corks are cheaper to manufacture, and also can keep the wine tasting better than traditional cork barks -- which sometimes fail and cause the wine to go sour. You open a bottle of wine with a plastic cork in essentially the same manner as a corked bottle: with a corkscrew.
Cut the foil at the top of the wine bottle with the blade on the corkscrew (or a knife if your corkscrew lacks a blade).
Insert the tip of the corkscrew into the top of the plastic cork. Begin turning it into the middle of the cork. It should twist into the cork easily. Don't press down on the cork, just twist until the screw is fully inside the cork.
Place the corkscrew brace against the rim of the bottle of wine. Press the handle of the corkscrew down. This will use the leverage of the corkscrew to pull the cork out. Some corkscrews have two levels on either side. In these cases, just push the two levels together to lift the corkscrew out.
Pour your wine into a glass and enjoy.