These things are but minor details that need to be worked out. Since revealing its brilliant idea, Zeroshift has found itself sitting on a mountain of investor cash and now employs a full staff of brilliant engineers striving to rid the world of slushboxes forever.
The dog ring sits between two adjacent gears and can slide over to engage the dogs of either one or can sit between them waiting to be useful. Here it's engaged in with the gear on the left.
The four dogs sticking out the side of the gear fit into the four slots on the dog ring. If I were king of the world, these slots would be called dog houses, but they aren't. Since the dog ring is splined to the input shaft (or it could be on the output shaft, but let's not confuse things too much) this dog-in-the-house arrangement locks the gear to the engine.
Notice how much bigger the houses are than the dogs. This way, if the gear is spinning a different speed than the dog ring, the dogs can still fall into the slots.
The three tabs on each gear are just like the dogs in a normal dog box. The blue and red things here are called bullets, but they do the same thing as the slots in a dog ring. This image has been simplified so your brain can handle it. In a real gearbox, there would be two bullets for every dog, there would be some sort of cage holding all the bullets and ensuring they spin with whatever shaft they're on, and finally, there would be springs encouraging the bullets to follow the cage when the shift fork yanks that cage toward the next gear.
Let's say the top gear is first and the bottom gear is second. In this position, the shaft is turning the bullets counterclockwise, so the blue bullet is pushing on first gear.
Here, the shifter has been moved, pulling the bullets toward the second gear. Since the blue bullet is interlocked with the last gear and only getting pulled on by a spring, it stays engaged. Meanwhile, the red bullet gets pulled into place between the dogs of the next gear.
Second gear is turning slower than first, so when the red bullet hits it, the bullets (and the whole engine) slow down. First gear, still going fast, pulls away from the bullets, setting the blue one free. Just like that, you're in second gear.