You can display the posts for a particular category simply by creating a menu item for that category. Just go to Appearance > Menus. If the Categories section doesn't appear on the left, click the Screen Options tab in the upper right corner of the screen and check Categories. Then mark which category you want to display on a page, click the Add to menu button, then drag & drop the menu item where you want to place it on the right.
If you want to add your category posts to a specific page that you've created, there are several plugins that will do that.