Stardew Valley

You will get your first bamboo fishing pole for free from Willy (it costs 500gold at his beach shop).

How to fish:
Face water with the pole selected, hold to start casting and then release at desired distance. When you get something to bite press to start the mini-game.
The goal here is to keep the fish inside the green bar. You control it by tapping or holding . Same as with farming and mining etc, this is a skill you level up.
Be aware some fish are harder then others to catch.

Depending on time of year/day and location you fish at, you will get different fish to bite.

Below is more detailed info thanks to idigitaltimes.com.
Link: http://www.idigitaltimes.com/stardew-valley-fishing-guide-ho...

Beach
Spring
Anchovies – 24/7
Eel – Early Afternoon or Night, when raining
Halibut – 24/7
Herring – 24/7

Summer
Crimsonfish (Legendary) - 6:00 a.m. to 10:00 p.m.
Halibut – 24/7
Octopus – Morning
Pufferfish – Early Afternoon, when sunny
Red Mullet – 24/7
Red Snapper – All Day, when raining
Super Cucumber – Night
Tilapia – All Day
Tuna – 24/7

Fall
Albacore – Morning or Night
Anchovies – 24/7
Red Snapper – All Day, when snowing
Sea Cucumber – 24/7
Super Cucumber - Night

Winter
Albacore – Morning or Night
Halibut – 24/7
Herring – 24/7
Red Mullet – All Day
Sea Cucumber – 24/7
Squid - Night
Tuna – All Day

All Year
Green Algae – 24/7
Sardines – All Day
Seaweed – 24/7
Trash – 24/7

Ponds
Spring
Catfish – 24/7, when raining
Legend - 6:00 a.m. to 10:00 p.m., in the lake near Marnie's Ranch

Summer
Pike – 24/7

Fall
Catfish – 24/7, when raining
Angler (Legendary) - 24/7, in pond north of Joja Mart

Winter
Catfish – 24/7, when snowing
Perch – 24/7
Pike – 24/7

All Year
Carp – 24/7
Chub – 24/7
Periwinkle – 24/7 (Crab Pot)
Snail – 24/7 (Crab Pot)

River
Spring
Catfish – 24/7, when raining
Shad– All Day, when raining
Smallmouth Bass – 24/7
Sunfish – All Day, when sunny

Summer
Dorado – All Day
Rainbow Trout – All Day, when sunny
Shad – All Day, when raining
Sunfish – All Day, when sunny

Fall
Catfish – 24/7, when raining
Lingcod – 24/7
Salmon – All Day
Shad – All Day, when raining
Smallmouth Bass – 24/7
Tiger Trout – Early Morning or Early Afternoon
Walleye – Afternoon or Night, when raining

Winter
Catfish – 24/7, when snowing
Chub - Day
Lingcod – 24/7
Perch – Day or Night
Pike – Day or Night
Tiger Trout – Early Morning or Early Afternoon
Walleye – Afternoon or Night, when snowing

All Year
Bream – Night

Other Spots

Arrowhead Island
Glacierfish (Legendary) - 6:00 a.m to 10:00 p.m., only during Winter

Desert
Sandfish - Between 6:00 a.m. and 10:00 p.m; year-round
Scorpion Carp - Between 6:00 a.m. and 10:00 p.m; year-round

Forest Pond
Carp - 24/7, year-round
Catfish - Mornings during Spring and Fall
Walleye - Afternoon and Night during Fall
Woodskip - 24/7, year-round

The Mines
Ghostfish – Floors 20, 60 and 100; 24/7, year-round
Ice Pip – Floor 60; 24/7, year-round
Lava Eel – Floor 100; 24/7, year-round
Stone Fish – Floor 20; 24/7, year-round
Sturgeon – Mine Lake; All Day, Summer and Winter only

Sewers
Mutant Carp (Legendary) - 24/7, year-round