This is how they arrived in DC World and Doctor Who World in Ryan's Quest: Chain of Memories.
They arrived in DC World
Ryan: I wonder where we are?
They saw Batman and Superman surrounded by Heartless
Ryan: Do you need some help?
Batman: Yeah, help us.
They are fighting the Heartless and they defeated them
Superman: Thank you for saving us.
Ryan: You're welcome.
Batman: And we have to save the city.
Evil Anna: Why?
Superman: Villains, of course. They take over the city now.
Batman: And we have to the other heroes to stop them.
Ryan: Can we help you?
Superman: Yeah, you can.
They went off
Matau: Bro? You think it will work?
Batman: This machine will get all the people memories back from the Villain's. And i have to test it first.
Superman: Do you think it worked?
Batman: Don't know, if we could try.
He press the button and it's not working
Batman: What the? What's going on?
He saw the fuel is empty
Batman: Oh, right. I need some fuel for this machine.
Superman: So, we have to get some more.
Batman: Yes, let's go find some.
They went off and they found some fuel for the Machine
Batman: We got the fuel.
Superman: Now, let's get to the machine.
???: Yeah, but it not gonna happen.
They saw the Villain's and they destroyed the Memories Machine
Joker: Hi, Batman!
Ryan: So you're cause of making People lose their Memories?
Two-Face: Yes, I am.
Batman: We're not gonna let you get away with this.
Harley Quinn: Oh, yeah? Fight us?
They are fighting them and they defeated them
Batman: Well, it will take so long for this machine to fix.
Ryan: Well, I guess we have to go.
Superman: Will you come back?
Ryan: Yeah, we will. Promise.
They left and they are in Doctor Who World and they saw TARDIS coming
12th Doctor: Hello.
Ryan: Who are you?
12th Doctor: I'm the Doctor.
Ryan: I see, nice to meet you.
12th Doctor: Come to the TARDIS. We have to stop the Dalek for draining all the People's Memories.
They went inside the TARDIS and they are in Dalek World
12th Doctor: We made it.
Ryan: Man, this place is in Ruins.
12th Doctor: I know, but we have to stop them. Come on
They went off to stop the Dalek Emperor for stealing the People's Memories and they found it
Dalek Emperor: Well, if isn't Sci-Ryan.
Sci-Ryan: My rival. We meet again. Again.
Dalek Emperor: And the Doctor.
12th Doctor: Let's battle.
They are fighting and they defeated it
12th Doctor: Excellent. Everyone from Earth got all their Memories back.
Ryan: That's great! But... What will you do now?
12th Doctor: Well, I'm going to find someone to help me.
Ryan: Sure hope you can find someone to help you.
12th Doctor: I will, Goodbye.
Ryan: Yeah, Bye.
They left Doctor Who World