How can you stop spotted hyenas from going extinct?

Spotted hyenas are Conservation Dependent according to the IUCN Red List. This means that they are not endangered, or even threatened. In the short term they are in little danger of becoming extinct, in fact they are probably the least threatened of all the large mammalian carnivores in Africa. However, in the long run, in order to reduce the likelihood of their extinction, a combination of research, setting aside large tracts of land as protected reserves, and working with local communities to improve animal husbandry and tolerate predators are probably the best hopes of any of the large African carnivores.

On a side note, spotted hyenas are not dogs. They are more closely related to cats, but are actually in their own family, Hyaenidae.