How do I do this?

Pick bananas for the guy in the plantation, put them in the crate, and then put your rum in there as well. Once you're back in Karamja, you gotta get inside that kitchen place.. I'm not sure if it's changed or not since RSC (last time I did it).

Yeah, that's briefly how it goes. Try reading the quest guide on the main Tip.it website. If I remember correctly, the guide writer did a pretty good job of explaining how it's done.

ok, I have the key, where is the blue moon inn?

It's in Varrock, i'm pretty sure its one of the buildings just south of the general store.