How did riku open the door?

[Ceriraye 485]

Ok so riku opened the door to the islands

But how?

Did he get the keyblade and open it?

How?

[heyitsdeven 131]

We actually don't know how/why he even found the door and opened it yet. Hopefully We'll get to see a flashback about it sooner or later!

[The Protagonist 332]

I assume its because he allowed the darkness to enter his heart so the door opened.Remember he did obtain the power of the keyblade but sora got when he let the darkness in.

[_The Door To Light_ 1,507]

Because darkness and stuff.

[J. Severe 1,137]

He said "open sesame."

[Wolf on the Run 391]

crowbar 

[Dave 5,715]

By being an ego-maniac with a deep seeded inferiority complex.