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Brunei has two mobile operators, b-mobile Progresif and DST. Both are privatized former state companies.
You will need to present your passport to get a prepaid SIM. Both companies have booths at the airport, and all mobile shops in BSB sell them as well. English is generally spoken in Brunei, although you don't really need it: showing them your phone and asking for a "prepaid SIM card" (in English) will get the message across just fine, and they'll set it up for you on the spot.
You're generally looking at around B$30 for the SIM plus credit. At time of writing, b-mobile offers a package that gets you 9 days of unlimited data for B$20.