Cut out a "window" in a wall separating the kitchen and dining room (Consult or hire a professional first to determine whether the wall is load-bearing). Finish the "cut" parts of the wall. Install an overhanging countertop on the horizontal cut-out surface and arrange stools under the counter overhang on the dining room side of the window. This approach to separating a kitchen and dining room is particularly appropriate if there is currently a wall between them that you don't want to remove entirely.
Install a dual-function breakfast bar with a prep counter and sink at hand level on the kitchen side and a raised breakfast-eating surface on the dining room side. This approach to separating the two rooms is especially suited to kitchens being designed from scratch -- or completely gutted and remodeled -- because such integrated breakfast bars can be large and unwieldy to install. Professional help can make major remodels go more smoothly.
Put in a stand-alone breakfast bar in the space between the kitchen and the dining room if you have a large, open area you want to section off. Ambiguous space can make a home look unfinished or awkward. Putting in a breakfast bar not only creates two visually distinct rooms, it can do so while also preserving the benefits of an open floor layout -- namely, a feeling of airiness and the option to reconfigure the furniture arrangement later.