Here is a guide to help you fish in the game, including a list of fish and a tutorial on how to fish.
Types of fish!
Anchovy – 1 Lunar Crystal
Tadpole – 1 Lunar Crystal
Carp – 3 Lunar Crystals
Coral crab – 5 Lunar Crystals
Turtle – 6 Lunar Crystals
Uncommon
Catfish – 25 Lunar Crystals
Supreme Turtle – 40 Lunar Crystals
Tuna – 41 Lunar Crystals
Crescent carp – 45 Lunar Crystals
Rare
Moon Jellyfish – 500 Lunar Crystals
Coelacanth – 1000 Lunar Crystals
Rough percentages
Uncommons appear in 13.60% of catches.
Rares appear in 3.20% of catches.
The sample size was 250, so expect some minor differences with your own results.
After equipping the luck sigil I did another 250 to see if it had any impact.
Commons appear in 78% of catches.
Uncommons appear in 18% of catches.
Rares appear in 4% of catches.
How to Fish
Well, i must first be the bearer of bad news. You do not immediately start the game with this feature unlocked. Across some areas you might see a sign with a fish on it, which teases the feature. But you do not truly unlock it untill around two hours into the game, and it is slightly hidden.
Step 1: find the fairy village
In order to even get the feature, you need to get the fairy village, as this is where the npc who gives you the fishing rod is.
Step 2: Follow the elevators down to the fishing pond
This is quite a long series of very slow elevators so patience is needed, but trust me its worth it!
Step 3: Talk to the fairy at the pond and enjoy your new gift from god!
Now you have truly ascended in life. May your finds be plentiful and be worth lots of munnies.