In case you didn't bring your own equipment you can buy weights, hooks and a fishing line at the shop Polynesia 2000 just below the church. Do as many locals and simply spin the line around a circular shape (such as a plastic bottle), place some bread dough (wet bread) or chicken meat on the hook and fling it into the ocean!
The most common, and luckily also one of the most tasty fish, is called nanue. On a good day, you might catch quite a few!
How Easter Island locals eat fish in the countryside
Make a strong fire and cover it with stones.
Open the fish by pressing a finger behind one of the two front side fins and tear it open. Rip out the intestines of all of your fish.
Carefully remove the gall bladder from the intestines. It is a long green string. Breaking it will ruin the intestines.
Clean the intestines as well as you can; push out the excrement by pressing the intestines between your finger tips along all of its length, then wash the intestines in sea water.
When the stones are hot, put the fish on the stones.
While waiting for the fish, cook the intestines on the stones as well, which is considerably faster. They are considered a delicacy.
When the fish is cooked, put it in the palm of your hand and eat with the other. The scales will come off easily.
When done, make sure you throw all bones, fins etc into the fire. This is mainly to please the vārua (Rapa Nui spirits), but as a bonus you'll keep ants from infesting the area.
...remove the fish scales. They protect the meat from getting burnt and dry.
...wash the fish in sweet water. Sea water is a natural spice and should be left on.
...leave the fish cooking too long. This will remove all the juice and flavor. Better is too raw than too cooked.
...leave any garbage behind. Leave the place as you found it.