It isn't so much as how you got there, because that is all your imagination and your mind just accepting it. Imagineers do try to transition us though. Sometimes it is very subtle and other times not so much. Tunnels & bridges are the most common transition.
Liberty Square transitions to Frontierland as if you are traveling from New England all the way to California. The official transition between the two lands is a small bridge that represents the Mississippi River. Splash Mountain threw this off a little bit, but we accept it.
Frontierland to Adventureland via Pirates is the blending of Spanish architecture from the wild west to the Spanish architecture of the Caribbean.
The transition from Hollywood Boulevard to Sunset Boulevard is just a street, but you switch decades from the 1930s to the 1940s. The transition is also supposed to reflect "date night" as you start the date off shopping around town until it's time to grab dinner (Hollywood Brown Derby) and take in a show. This explains why many facades on Sunset Boulevard are theaters. All leading to the end of the night at the romantic hotel.
Toy Story Land is more abrupt, but you'll notice the transition of lots of "grassy" plants and the change in concrete. On the Galaxy's Edge side, you'll notice how the Toy Story Land side had toy versions of the same lamp posts that the Galaxy's Edge side does. You might be able to infer that Galaxy's Edge might just be more of Andy's space-themed playsets like his Buzz Lightyear one nearby.
Most World Showcase countries have abrupt transitions, but the transition from the UK to France is supposed to represent the English Channel. I've also heard that Mexico and Canada are the first countries we come to, because they are our neighbors here in the US.
In Asia, you transition from the low lands of Asia (India) and you trek toward the highlands as you get closer to Everest. The pathways gentle incline and you can see it in the concrete where you go from mud to more of a rocky path.
Future World transitions had the breezeways that led into the different sides of the brain: the left side was the analytical side with computational fields like energy, health & medicine, transportation, inventions, and space exploration. The right side was more emotional and natural with the seas, the land, the arts, and our imagination. The walkways and landscape even showed this. Pathways are curved on the right and angular on the left. Then leading into World Showcase is the world at our senses in front of us.