I'm a little confused

[Arina]

All these bugs are roaming the island and there's fish and such but since you can't take your net or fishing pole, or wet suit, how are you supposed to catch anything there?

 

[Enpsychopedia]

Talk to the gyroid.

 

[kittenrobotarmy]

The Gyroid next to the hut when you exit lets you take a net, fishing rod, wet suit, axe and shovel free of charge.

 

[StarryACNL]

I have not tried this but you could put your equipment in the box and take it that way.
However you need to remember to put it back or you will lose it.

The simple way: talk to the groid.

 

[kittenrobotarmy]

I have not tried this but you could put your equipment in the box and take it that way.
However you need to remember to put it back or you will lose it.

The simple way: talk to the groid.

The box only transports things from the Island to your town, not the other way around. You can't put anything in the Box at your town anyways.