A very common question experienced GMs ask me about these games is "how do you deal with people who aren't, like, into comics, when the whole idea of these anthologies is to create a comics-style anthology?" 

In the mid-2000s when Marvel Comics was making their big push to digital creation and distribution of comics, each Marvel comic carried on its first page (or on the inner cover) a short summary of what you needed to know before you read the comic you just bought.  Sometimes this was four paragraphs (as when you just bought the second to last comic in a X-Men series), sometimes it was one sentence (as when you just bought a standalone Spider-man comic.)  I was sort of surprised that the fans didn't seem to see what a clear indictment of "continuity" this practice was, at least as comics fans commonly understood it.  

The actual creators of Marvel comics saw continuity as a set of tools from which they could select a lot of material, a little, or nearly nothing.  As far as I can tell, they still have this attitude, and it's common at DC as well.  Only comics fans cared about continuity beyond its immediate impact - the impact on the dramatic or comedic elements of the characters and situations immediately in front of them.  The creators - the artists and writers - wanted to tell the stories they wanted to tell; continuity was a tool they might call upon - reach into the toolbox and pull something out - but they didn't want to worry about the full history of the comic book world.  They felt perfectly comfortable misuing, misremembering or misstating things that had happened in the "past" of the comics.

This approach, I have found, is absolutely necessary in tabletop RPGs based on these types of highly detailed and long-established settings.  In a tabletop RPG, play covers action about as quickly as it does in monthly comics.  You can't spend your time going into the deep history of each character, not because you might not like it, but because there is no real possibility that the full continuity of a complex world could ever truly be relevant to an exciting, fast-moving adventure.  (This philosophy, to an extent, is discussed more in depth in Champions Now.)

Thus, the key issue when you deal with introducing a character into a tabletop RPG isn't a conveyance of a complex continuity, because that's not truly necessary in an exciting comic book.  In comics, the relevant characters and events are simplistic and iconic.  Instead of conveying continuity, what you need to convey is a reassurance to the players that they are equal creators with the originators of the characters and plots of the established setting.  The GM and players will make Batman and the Joker and the Riddler who they need them and want them to be.  The corporate owners of the characters have no say in it.  

Do you think Spoiler got a raw deal?  Of course you do, everyone who is reading this thinks that.  If you don't think Spoiler got a raw deal from DC Comics you wouldn't have ever found your way here, I promise.  In a tabletop RPG, your view of Spoiler is actually more significant than DC Comics' view.  You and your fellow collaborators get to make that character just what you want her to be.  Once you have that in mind, that becomes what continuity actually is, just like the way Marvel Comics would sometimes just summarize the last 60 years of Spider-Man continuity by saying "we're about to have a fun adventure with your friendly neighborhood Spider-Man!" You decide what the continuity both of the character and the world is, because comic book continuity is not an ironclad beep-boop set of actions and consequences and historical analysis.

There are two types of game continuity setups that are commonly used to try to reassure players into feeling this power.  The setups aren't necessary, exactly, but they're common enough that people look to them quite a bit to discuss how continuity is used: Year One, and (what I have termed) "Year Two".

Why Year One?

"Year One" campaigns are those in which the player characters are created and have their early adventures at the same in-game time as the established characters in the setting have theirs - they may help Harvey Dent with his campaign against corruption before he becomes Two-Face, they may believe in Lex Luthor's scientific propaganda before he is revealed to be evil.  The advantage of such a campaign is twofold - people don't need to know much about continuity, and indeed, can become significant figures in the lives of NPCs who will then have things that they want and expect from PCs.  

My first stab at an anthology campaign attempted the Year One approach. It's certainly a possibility.  But my greatest success has been with "Year Two."

Why Year Two?

"Year Two" games (defined by me, not related to the Year Two graphic novels) are the same as Year One games but there are no origin stories - Two-Face is already Two-Face, the Joker has already established himself as the clown prince of crime.  This retains the advantage of not needing to know about continuity, but still having a full panoply of characters immediately available - if someone watched the Harley Quinn cartoon and laughed at King Shark or something, you can bring him in.  

I eventually landed on Year Two games for this anthology, but not because it was easier or harder for players who weren't familiar with comics.  As I mentioned above, these characters and events aren't what you'd call deep or complex, in terms of how they might impact a player character's story.  No, I landed on Year Two because it freed me to enjoy all the various permutations I've absorbed of these characters over the years! It really did help my own sense of satisfaction to be able to just casually say "yea, in this world, it's known that aliens and ghosts exist because they're like...on the news sometimes" and then go from there rather than go through "reveals" of continuity-to-come. It just felt better to me to have all of Gotham City instantly at my fingertips, even if it the other players wouldn't really care so much about it.  And that's where we ended up!