The Gapuri have multiple ways of saying certain letters or syllables (which in their language can be shown as a single symbol). I'll focus on "g" for now.
They use a combination of their throat muscles and back of the tongue to create the "g" sound in "Gapuri." The constrict the top of their throats, sealing off the esophagus and trachea, and push their tongue back to create a bubble, which they pop loudly when they move their tongue down and forward while raising the back of their tongue, this moves the bubble forward. This expels the sound forward out of the mouth rather than backwards into the throat.
Bubbles are used somewhat frequently to create different types of sounds. Their language is not made up entirely of sounds they make with their vocal cords, they also use jaw clacking, tongue clicking, and gusts of air to create whistle noises.
The "g" sound accounts for the "Ga" part of the "Gapuri," the "p" sound is soft and airy. Since they do not have a lower lip with which to create a hard popping noise the sound is much different than the Human "p" sound. To make the sound the Gapuri press their upper lip to their mandibles (which are also pressed together) while pressing their broad, manipulatable tongue to the bottom of their jaws (this seals any gap between the mandibles) and fill their mouth with air. Then they build some air pressure up in the front of their mouth and quickly release it by moving the upper lip. This is the "pu" part of "Gapuri."
The "Ri" part is fairly simple as they can pronounce is much the way a human pronounces "r" and "i" noises.