This mini guide covers Wild World, City Folk & New Leaf, and should help novice fishers out with their skills. Not applicable to the GCN game or previous titles, as their fishing mechanics are different.

Basic cast
Basic speaks for itself. Aim the lure just forward of the fish's head.

Motion cast
Same as basic cast but used when fish is moving straight. Distance between lure and fish should be roughly doubled so to account for fish's change in position. Halfway there the fish will become aware of the lure.

Slice
Use when fish is at a sharp angle to the land. Almost like hitting a tennis ball with the racquet angled, you either want to wedge the lure beside the fish or past the fish.

Step-back
If the fish is too close for your range, move back a pace or so to correct distance.

Reversal
Fish often are still or moving straight, but when they're not, they're turning. If you predict this or see sudden movement, aim to the opposite side where the fish wil turn and get handily lured.

Direct hit
The angle or position can often be too poor for even a slice cast. So aim exactly for the fish's head or body; this will send it moving (and does not cause it to flee).

Further tips not pertaining to casting in particular soon to come.