Where to Find Information About Carbs at Burger KingThere is a nutritional information brochure at Burger King, but it won't tell you about custom options such as ordering a burger without the bun. But some of that information is available online:
Tips for Carb Counters (PDF): Burger King menu items that are low in carbs, and how to customize your order to cut carbs.
Nutritional Information (PDF): Information, including carbohydrates, on all the standard Burger King menu items. Unfortunately, there is no way to tell about the individual components McDonald's does this, and it's very helpful. You might be able to guess about the condiments by looking at the McDonald's tool.
Ordering Burgers at Burger KingObviously, ordering burgers without the bun is the way to go. You will get the burger in a plastic container with most of the condiments. As with many other places, mayo seems to be considered a condiment for the bun, not the burger, and you won't get it unless you ask for it. You may have to ask for a knife and fork to go with it. Hamburgers have zero carbs, but some of the condiments have carbohydrate. Other than saying that the ketchup has 3 grams of carbohydrate and the mayonnaise zero, BK does not give information about the condiments.
Other SandwichesThe best bet on other sandwiches is the Tendergrill Chicken Sandwich without the bun at 3 grams of carbohydrate. If you get the Veggie Burger bunless it will cost you 19 grams of carb, and the rest go up from there.
Salads at Burger KingSalads at BK are, unfortunately a little disappointing. In particular, the side salads are almost entirely iceberg lettuce. A thin slice of tomato and a few tiny carrots complete the "Garden Salad". The base for the meal salads is a little better, as it has the more-nutritious romaine lettuce included.
The only low-carb meal salad option is the Tendergrill Chicken Garden Salad, at 8 grams of net carbohydrate (not counting dressing and skip the croutons). The Tendercrisp Chicken Salad has 23 grams of net carbs.
The dressings, as always, contain a wide range of carbohydrate. The best one is the Ranch Dressing at 2 grams of carbohydrate per packet. (Do NOT get the Fat Free Ranch Dressing, as it contains 15 grams of carb!) The Creamy Caesar and Light Italian dressings could also reasonable choices, at 4 and 5 grams, respectively. And you don't have to use the whole thing, of course.
Sides and DessertsThe only real possibility is the Fresh Apple Fries (which aren't fried, BTW) at 5 grams net carbs. Skip the caramel sauce of course.
If you just want a Chicken Tender or two, they are a little over 2 grams of carb apiece. Choose the Ranch dipping sauce at 1 gram per container.
BreakfastThere are a couple of omelet sandwiches that you could get without the bun, but there is no information about carb counts in that case.
BeveragesObviously water, diet sodas, and coffee are the zero carb options (or almost so). Don't be tempted by the iced coffee, with a diet-busting 66 grams of carbohydrate. And believe it or not, the shakes go up to 154 grams of carbohydrate and 960 calories!!
With care, an occasional meal at BK won't break your diet, but there isn't enough nutrition available there to make it a habit.