As with culture, it's difficult to pinpoint Slovak cuisine with any certainty. If you had to generalize you'd be safe in saying it's similar to Czech and Austrian cooking, but spicier, more adventurous, and often better tasting. That means lots of meat dishes, with beef, pork, and chicken popping up on menus most often, but with a fiery taste that's often lacking in the countries to immediate west.
Many meals are built around the ubiquitous halusky, the Slovak equivalent of dumplings in the Czech lands. Halusky are little noodles made of potato meal, flour, and egg, which are then boiled and served as mains or sides. The national dish is bryndzové halusky, where the halusky share equal billing with a deliciously sharp, sour sheep's cheese and small chunks of bacon.
Mealtimes hold to the Continental standard. For breakfast (ranajky), Slovaks take a light meal that may only consist of a bread roll with tea or coffee, though hotels and pensions typically offer the standard table of cold cuts, cheeses, and cereals. Lunches are larger and usually served from noon until 2pm. Here you'll usually be offered two courses: a soup (polievka) and a main dish. Common soups include a deliciously sour cabbage (kapustnica) and vegetable (zeleninová). Mains are usually built around meat of some kind, with pork (bravcové) the most common, followed by beef (hovadzie) and chicken (kurca). You'll usually be expected to order a separate side dish. Potatoes (zemiaky) are the most common, usually served boiled or as fries, or something called "American potatoes," essentially large fries served with the potato skin intact (like steak fries). Dinners are more substantial, consisting of an appetizer, main course, and dessert (dezert). Desserts are normally built around pancakes of some sort, usually featuring chocolate and nuts, or fruit jam.
Vegetarians will find Slovak restaurants disappointing. Most restaurants offer salads, omelets, and fried cheese, but few if any meatless entrees. Menus typically include a section called "Meatless Dishes," but curiously these, too, generally contain a piece of ham or bacon.