If you need some medication (as I did during my stay) and you know what you want the obvious place to go is a pharmacy/chemist shop. I went to Guardian in the centre of town...but they don't stock drugs such as antibiotics.
For those you need to go to a dispensary, and there's one across the street opposite Guardian, called Yin Onn Dispensary.
The two ladies there speak good English and they provide things such as antibiotics without a doctor's prescription. Cost was not high - amoxycillin worked out at B$1 per capsule (B$10 for a strip of ten).
Aboiut 200 metres from the town centre is a new, permanent, undercover market. It's very easy to find, it's a large single storey building with a bright blue roof and it's on the main road into town, Jalan Sungei.
When we were in KB in November 2011 it had only recently opened and some of the stalls were not yet operating.
What to buy: There's a section for fresh fish, another for fruit and vegetables, another for general non-food items.
There's a good weekend wet market just outside the town centre, something like one kilometre, with plenty of stalls selling fruit, vegetables, fresh fish and a small section with a handful of stalls selling plants and flowers.
You'll see fruit and vegetables that you may not have seen before, and its great for photography because I've never seen another market where the products are displayed so neatly and carefully.
What to buy: If you're staying in a hotel you won't need the vegetables or fish, but the fruit is fresh and inviting. We bought rambutans, bananas and mangos but there was plenty of other fruit available too.
What to pay: Depends what you buy of course but it's all very cheap, just a few Brunei dollars.
The largest shop in town is a combined supermarket & department store and you'll find most of what you need there.
What to buy: The ground floor supermarket is well stocked with both local/regional and western products, with the usual range of supermarket items.
The first floor has clothing and the second floor has everything else - electronics, furniture, stationery, souvenirs etc.