So far we've talked about travel through the air, over the water, and across the land. But now we traverse into a bold new territory: Dimensional travel. So obviously this may not be applicable to every type of game, though a surprising number of campaigns and systems make room for one kind of dimensional journey or another. These voyages are more complex but can also be even more rewarding than more mundane modes of travel, so let's jump right in.
Meaning: First and foremost, when you're talking about journeying to another dimension it's important to decide what exactly that means. Are the players venturing into an alternate version of their own world? Will they meet their own evil or bizarre counterparts? Are they venturing to another plane of existence where the fundamental rules of physics are different? Are they literally reaching another dimension in the sense of becoming two or fourth dimensional (or more). All of these choicr can lead to some very different and very exciting options, but it's crucially important to decide how these dimensions work. Are they infinite in scope? Are there an infinite number of them? Consider the answers to these questions and the implications of those answers right from the outset.
Method: How are the players getting to another dimension? Do they need to follow tunnels into the depths of the earth and walk a secret passage into Hell itself? Is there a great machine built by ancient beings that can tear a bleeding hole in reality? Do they have the power of a magical pixie that lets them become two dimensional? Is it as simple as a mad scientist with a portal gun or as complex as an entire campaigns worth of preparation?
Description: One of the most important among a GM's jobs is to explain the surroundings of the players. When they venture into a strange world entirely foreign and bizarre that is no small task. Always remember the five senses when setting a scene. Touch, Sound, Sight, Taste, and Smell. Give that to the players and let them drink in the feeling of this strange new realm. Even in a modern setting, something as little as, "The scent of fried chicken fills your nose, But in this world, Kentucky Fried Chicken smells like McNuggets." Is enough to send a shiver down the players spines and fill them with a sense of wrongness.
Encounters: When it comes to interdimensional peril, there is literally no limit to what you might want to throw at the players. Always remember however that a change of locale can be very disorienting and can change fundamental aspects of encounters. A barbarian who has absolutely annihilated every foe thus far with their war hammer might find a little bit of extra challenge on an elemental plane of water, as might a wizard who relies on verbal spell components. Likewise a smooth talking lawyer might find it hard to talk their way out of a run in with a posse of werewolves when the laws and people they know don't exist. And needless to say, if your players get teleported to a dimension with roiling lakes of fire you had better put a darn guardrail up or be ready for a player to fall in the lava.