Mostly the natives were Shoshone and related tribes, Utes, Paiutes, and Gosiutes. They lived a hunter gather lifestyle revolving around hunting the smaller Intermountain herds of bison and other big game and seasonal nut harvests. There were also some Navajo and Apache in SE Utah. There had been some European visitors to the area, mostly explorers and trappers, including some temporary trading posts, but there weren't any permanent settlements prior to the Mormons.

The arrival of the Mormons were initially a mixed blessing. They quickly turned into valuable trade partners, and groups that traded with the Mormons became wealthy and influential compared to their neighbors. The Paiutes in particular were friendly with the incoming Mormons and there were several intermarriages. But the Mormons occupied some of the richest areas. This lead to starvation among a lot of the native tribes as they couldn't maintain their traditional way of life. Likewise disease tore through the natives. The Paiutes for example lost roughly 90% of their population in the 1850s as successive epidemics of cholera, scarlet fever, whooping cough, measles, mumps, and tuberculosis ripped through them. To his credit Brigham Young did encourage his followers to feed and otherwise help these tribes as best as they could. But the situation remained tense. Eventually this led to confrontation culminating in the U.S. army and local militias committing the Bear River Massacre against the Shoshone and eventually the Black Hawk war. The other tribes were even less populous than the Shoshone and were forced to capitulate without even a named war. The natives were eventually forced onto reservations, generally in areas considered waste lands by the white settlers.

So basically it followed much the same pattern as natives across most of North America.