You can cast a line by pressing "CAST" button on the lower right corner.
After doing so a fishing minigame will start, in it, you have to manipulate the reel to keep the energy bar from fully filling and emptying. By keeping the power level in the smaller window you will earn combo points.
The more combo points you'll get the more points you will earn for catching that fish.
Fully filling the combo bar (up to 100%) will result in 5% more points.
After successfully catching a fish you will see all information about your catch:
Size, rarity, weight, earned points and coins. By pressing "Claim" button points and coins will be added to your account.