Most carbs come from vegetable matter, dairy has varying amounts of carbs too - always check packaging for nutrition info, ignore the sugers bit, its the total carbs you need to look for.
Meat and fish have very little carbs, in fact for some types practically none. Same for cottage cheese.
When it comes to processed foods Low fat usually equates to high carb unfortunately as with no carbs and no fat food pretty much has no flavour, so they replace the fat with sugers, carbs and salts.
Low carb does not have to mean no carb. Root veg tend to be high in carb. Green veg are fine, celeriac and cauli is fine, peas are not so good. There are online resources and also some good books on the subject that list foods with carb and calorie values.
I actually increased the amount of veg I ate when I went from medium carb to low carb, mostly because I cut out potatoes, flour based products, rice and pasta.
I also lost weight and now am about right for my height and build, and my cholesterol and trigs are much lower. Fats (other than trans fats are not your enemy when it comes to cholesterol and triglycerides, and its excess carbs rather than dietary fat which ends up as body fat.