Short answer: Open the bail, pinch the line with your index finger, swing the rod, release at 11 o'clock. When you feel a bite, lift the rod sharply with one motion. Don't yank repeatedly.
Hold the rod with the reel under the rod, not over.
Reel until the bait hangs about a foot below the rod tip.
Open the bail (the wire arm that loops around the spool). It will swing up and click into the open position.
Pinch the line against the rod blank with your index finger. This holds the bait in place while the bail is open.
Point the rod tip at where you want the bait to land.
Bring the rod backward over your shoulder smoothly.
Swing it forward in one motion. When the rod tip points roughly at 11 o'clock and the rod starts to load up, lift your index finger to release the line.
The bait flies out and lands. Reel the bail closed (most reels do this when you turn the handle once).
The biggest beginner mistake is casting too hard. Twenty feet is plenty for bluegill on a dock. A short, controlled cast that lands where you want beats a 50-foot cast into the wrong place.
Most beginners also forget to release the line at the right moment. Release too late and the bait shoots straight down. Release too early and it shoots straight up. Practice on grass before you try it over water.
Sidearm casting (under docks and trees)
Same motion as overhead, but the rod stays low and parallel to the water. The bait skips along the surface like a flat stone and slides into shaded structure (under a dock, under overhanging branches, behind a laydown). It's the cast that catches bass under cover.
Sidearm is harder than overhead. Practice on open water until the bait lands where you want, then try it under cover. Don't try this for the first time on a dock; you'll hook the dock or hook yourself.
Vertical jigging (no cast at all)
From a boat or a high dock, you can skip casting entirely. Drop the rig straight down next to a piling or over deep brush. The motion:
Open the bail, let the line out until the jig touches bottom (you'll feel the line go slack).
Close the bail. Reel up just enough that the jig is a foot off bottom.
Lift the rod tip slowly about a foot, then let the jig fall back on a tight line.
Watch the line and the rod tip. A bite often shows as the line jumping sideways or the rod tip taking weight unexpectedly.
This is the highest-percentage technique for crappie under Watts Bar docks. Slow lifts, not jerks.
What a bite feels like
Different rigs feel different.
Bobber rig: the bobber goes under, twitches sideways, or lays flat on the water. Wait one full second so the fish takes the bait, then lift the rod sharply with one motion.
Bottom rig: the rod tip taps. Sometimes hard, sometimes barely. Pick up the rod, point it at the fish, reel in any slack until the line is tight, and lift sharply. With circle hooks, don't set hard; just keep tightening.
Lure (jig, soft plastic, crankbait): the rod loads up unexpectedly, you feel a sharp tap, or the line jumps to the side. Set immediately and hard. Lure-fish are usually swimming with the lure when they hit; if you wait, they spit it.
How to set the hook
One sharp upward motion of the rod tip. Don't yank repeatedly; the hook is either set or it isn't.
If you miss the hookset, drop the bait back into the same spot immediately. Bluegill especially will hit again within seconds. Bass and crappie will sometimes follow up too if the lure stays in the strike zone.
How to fight, land, and unhook a fish
Once the hook is set, keep tension on the line as you reel in. Don't let it go slack; the hook will fall out. Don't horse the fish (jerk hard); the hook will tear free.
For bluegill-sized fish, just lift them out of the water with the rod. For anything heavier, lift with the rod and slip a hand under the belly to support the weight before bringing the fish over the rail. From a high fishing pier, use a landing net with a long handle.
To unhook: wet your hands first (dry hands strip the fish's protective slime coat). Hold the fish gently around the body, not by the gills or the eye sockets. Use pliers to grip the bend of the hook and back it out the way it went in.
If the hook is deeply swallowed and you can't see it, cut the line as close to the hook as you can and release the fish. The hook usually rusts out in a few weeks and the fish survives. Trying to dig out a deeply-set hook does more damage than leaving it.
To release: support the fish in the water until it kicks out of your hand on its own. Don't drop it from height. Don't toss it back in.
For grip-by-grip on different species (and what to do about catfish spines), see handling fish safely.
Either the bail is closed (open it before casting) or your finger isn't holding the line (pinch the line against the rod blank with your index finger before swinging). With both done correctly, lifting the finger at the right moment in the swing releases the bait. See gear troubleshooting for more.
How hard do I set the hook?
One sharp upward motion of the rod tip, hard enough to drive the hook past the barb. Don't yank repeatedly; the hook either set or it didn't. With circle hooks, don't yank at all; just keep the line tight as the fish swims off and the hook sets itself.