The reproductive strategy is called adenotrophic viviparity. A single egg hatches inside the female, and the larva is nourished by a specialised accessory gland that secretes a fluid rich in protein and lipid, functionally comparable to milk. The larva passes through its instars entirely inside the mother.
When it is deposited it weighs about as much as the female herself and burrows immediately into loose soil or shade litter, where it forms a puparium within roughly an hour. A female produces a new larva every week or so and only around eight to twelve in a lifetime, an extraordinarily low output for a fly.
That low reproductive rate is the reason tsetse control by sterile insect release and by trapping can work at population scale where it would fail against a fly laying hundreds of eggs. It also means the flies depend on a gut symbiont, Wigglesworthia, to supply vitamins absent from a diet of pure blood.