The Multiverse is a boundless expanse of worlds. These worlds, called planes, are as different from each other as one living being is from another, varying in size and shape, inhabitants and environments, and even the laws of physics and magic. The existence of magic, though, is a common factor that unites all the known planes.
For most inhabitants of a given plane, that plane is the full extent of existence. Esoteric speculation might posit the existence of other worlds, but such concepts are only theoretical. Only a handful of people on any given world know the reality: that all the planes are suspended together in a void called the Aether—or, more poetically, the Blind Eternities. Only one person in a million is born with the potential to travel from one plane to another, and only a fraction of those with the potential actually manage to ignite their sparks and become Planeswalkers.
Often, this happens as a result of a great crisis or trauma. A near-death experience could ignite the spark, as could a life-changing epiphany or even a revelatory trance. But once their sparks are ignited, all Planeswalkers gain the rare ability to open a pathway through the Blind Eternities and pass from one plane to another.
The life of a Planeswalker is a life of choice and self-determination, unrestricted by the boundaries of world or fate. Most Planeswalkers dedicate themselves to some personal mission as they explore the secrets of the Multiverse. Often, they discover the depths of their own souls in the process.
This is the fourth Plane Shift article (corresponding to the release of the fourth volume of The Art of Magic: The Gathering), which means that at this point, you could put together a four-person party of Planeswalkers and have each one of them come from a different plane.
Fundamentally, no game rules are attached to being a Planeswalker. Traveling from plane to plane in this sort of campaign is a lot like overland travel in a normal campaign: it's about getting to where the adventure is. It's a story function, not a rules one. If planeswalking is part of the campaign, then everyone in the party has to be able to do it, so they can travel together. (In modern Magic, there's no way to bring another living person along with you when you planeswalk.) That means there's not really any question of game balance where planeswalking is concerned—it doesn't make one character more powerful than another, and it doesn't make characters any stronger against the enemies they're fighting. So it's something that can be added on to any other character, without changing the character's class, race, or background.
How does planeswalking work? Well, despite the name of this article series, it actually doesn't bear much resemblance to the plane shift spell. When characters planeswalk, it usually takes prolonged focus to bring two worlds together and create the bridge to cross between them. This process takes about a minute and is similar to casting a ritual, so it's not generally something that Planeswalkers can do to escape combat. It also doesn't allow for much precision. As a rule, the point on a plane where a Planeswalker arrives is up to the DM, and it's usually the same location for each visit a character makes to a plane.
Occasionally in Magic fiction, characters do planeswalk in the middle of combat, usually when something dire is about to happen. (That includes the circumstances when a character's Planeswalker spark first ignites.) To model that, at the DM's discretion, a Planeswalker who is about to drop to 0 hit points can make a Charisma saving throw with a DC equal to the damage taken. On a successful save, the character instead takes no damage and planeswalks away. It's up to the DM what plane the character ends up on, because this isn't usually an intentional process.
You could do a lot of adventuring on just the four planes detailed in the art books and Plane Shift articles so far. But if you want to take your Planeswalker characters to Theros, Tarkir, Ravnica, Dominaria, Mirrodin, Alara, Fiora, Lorwyn, Kamigawa, or any other plane in the Magic Multiverse, you can follow the example of what I've been doing in these articles. Reskin and tweak existing monsters, and inject a healthy dose of creativity and improvisation as you go. Some of those worlds are full of creatures that could have stepped right out of the Monster Manual, while others will present a greater challenge.
The most important thing is that a campaign involving Planeswalkers requires an agreement between the players and the DM. Even more than usual, if the players decide to ignore the plot hooks set before them and go off anywhere in the Multiverse just because they can, they can make the DM's job more taxing than fun. It's one thing to have a Planeswalker pop off to Ravnica for an hour to buy a cup of coffee, but it's quite another for the players to decide that they want to take on the corruption of New Phyrexia today, instead of following clues that lead clearly to an Innistrad campaign.
Speaking of New Phyrexia, a campaign with Planeswalkers is generally more fun with higher-level characters. The Planeswalkers who feature in the stories of Magic are powerful mages of various kinds, and their actions can sometimes decide the fate of whole planes. It doesn't always need to be like that, of course, but it can be hard to motivate characters with the ability to travel literally anywhere to stick around and root out a nest of giant rats.
So can Planeswalker characters travel from Amonkhet to whatever plane the Forgotten Realms lies on? That's up to you. The Plane Shift series more or less assumes a certain continuity from one Multiverse to the next, even as (for example) it makes no attempt to model Magic's five colors of mana in the D&D magic system. So there's no real reason an elf from Evereska couldn't "spark out" and find herself on Kaladesh, as long as it works for your players and your campaign.