There have been lots of threads in the past on Insurance, and you are right, it is a minefield!
Generally, policies don't cover routine treatment - vaccinations, neutering and the like - and there are various types of cover; those that cover a pet for each condition for a set length of time (often a year), those that cover each condition for a set value, and those which offer "cover for life" for each condition with no maximum limit set. Some policies cover extras like alternative therapies or behaviourists - the cost of the premium usually reflects what you get, and they vary hugely - you can pay as little as £10 a month, or as much £40
If your pup/dog has seen a vet before you take out a particular insurance, you must declare this when you insure them - policies often contain exclusions - conditions that the insurance company won't cover because they have been treated already
Premiums do go up year on year; usually reflecting the increased costs of veterinary care that they are used to cover and also as a dog ages, it is more likely to need treatment - but the costs don't generally go up if you make a claim