One can become a werecoyote by inheriting the trait from their parents. It is presumed one can turn into a werecoyote by being bitten by an alpha coyote, though this is not confirmed. Also like the wolf, a werecoyote functions best by being part of a pack. Their animal instincts, powers and abilities are also at their strongest on the full moon.
Series
Malia Tate is a born werecoyote who first appears in Season 3 and later joins Scott's Pack. In Season 5, one of the major antagonists Theo Raeken, is a Chimera with the traits of a werecoyote as well as a werewolf. Corrine, Malia's birth mother, known by the alias, the Desert Wolf, is also a werecoyote.
Supernatural traits & powers
Like all canine werecreatures, when a werecoyote follows an alpha, joining his pack, they receive symbiotic maturity and power by being a packmate. They become more accomplished in using their supernatural abilities, their powers amplifying and their self-control and prowess improving. Malia Tate, as a member of Scott's Pack, with Scott being her alpha, her preternatural strength, endurance, speed, agility and skill with using her supernatural abilities have improved since joining. Her eyes also flash blue in response to Scott's alpha's roar, displaying she becomes stronger from the support of being in his pack, establishing herself as a beta werecoyote.
Werecoyotes, like their werewolf cousins, feel a strong camaraderie and kinship towards their own. In Season 5, Malia was the first in the pack to put trust in newcomer Theo Raeken who put himself out as a werewolf wishing to gain entry into the pack. Though she was none the wiser, this was due to Theo's werecoyote part gravitating her towards him. Theo also admitted to Malia he'd felt regret when he sold her out to Corrine, despite his being a sociopath and had no trouble betraying and manipulating the rest of Scott's pack and allies. This admission on his part indicates Theo felt artificial remorse for betraying a fellow werecoyote.
Likewise, Malia immediately identified the Desert Wolf from her recovered memory. It's likely she knew the woman she saw at the time was her biological mother, not only because Corrine is a werecoyote like her, but also because she's Malia's birth relative.
Similarly, a werecoyote receive symbiotic power from their own kind. In a case specific to them, when a coyote mother gives birth, part of her power is passed to her child. If the mother were to take action on a full moon, they can take back this power. This happened when Corrine gave birth to Malia and most of her power was transferred to her daughter.
Transformation
The werecoyote's transformation consists of two shapes: a full animal coyote and the commonly seen near-human shape.
Malia Tate had shapeshifted to her full coyote form for the first time when she was nine years old. Her transformation was triggered when her family's car was run off the road, the resulting trauma, upheaval and it was the night of a full moon. Because to her age, and the horror of her family's deaths, Malia was unable to transform back to human and remained a coyote for the next eight years of her life.
Malia finally returned to her human form only because of the intervention of Scott McCall's alpha roar.
The chimera Theo Raeken is able to shapeshift into the full coyote form seen in 5x10 - Status Asthmaticus. He was scientifically enhanced by the Dread Doctors, contributing to this.
In The Divine Move, Alpha werewolf Scott is shown to have taken Malia Tate into his pack. He is also seen teaching her how to shapeshift, starting with morphing her claws. A few months afterwards, she's now able to manifest the coyote's near human shape, as well as control it, rising to beta werecoyote status. She also manifests this shape in the face of danger, as well as during the full moon.
The wolf/coyote Chimera, Theo Raeken commonly manifests the near-human shape. He can harness either shape due to being created from the Dread Doctors' experiments.