what rain does
Rain covers every surface biome at once and lasts anywhere from 8 minutes to just over an hour, averaging around 20. Most of it is atmosphere: dimmer light, heavier cloud cover, different music, and enemies turning up in raincoats or holding umbrellas. Goldfish climb out of the water and shuffle around on their tail fins. In a Snow biome the same event renders as a blizzard, with thicker snowfall and a visibility effect that makes your character squint.
It adds no water. No new liquid tiles appear, existing pools do not rise, and lava and honey are untouched. The three intensities, light, regular and heavy, only change how dark the world gets, and one storm can shift between them several times. A Weather Radio tells you which is running, and it reports the surface even when you are deep underground. Town NPCs stay home for the whole storm, exactly as they do at night, so shopping means walking to their doors.
the fishing window
Rain gives a flat 20 percent boost to fishing power in every body of liquid, which is the one solid mechanical reason to care about it. That stacks on top of your rod, your bait and a Fishing Potion, so a rainy stretch is when you burn Crate Potions or go after a quest fish that has been ignoring you.
Worms surface in Forest biomes in real numbers during rain, which is free bait if you carry a Bug Net, but they only spawn where the sky is open. Roof your fishing hole and the worms stop coming, even though the water underneath still counts as rained on. Waterleaf also blooms for the duration, and blooming is the state you have to harvest it in to get seeds back, so a pass along the desert oases during a storm is worth more than the same walk on a clear day.
what comes out in the wet
Rain brings its own spawn table. Several regular enemies get rain variants, and a few only exist while it falls: the Umbrella Slime on the surface, the Flying Fish in Hardmode, and the Angry Nimbus, which is the only source of the Nimbus Rod. If that weapon is what you are after, you need an open surface in a Hardmode storm, not a bunker with a roof.
The extra spawns cut both ways. During a Blood Moon or a Solar Eclipse the rain enemies compete for the same spawn slots, so the event enemies you were actually farming appear less often. If it starts raining halfway through an eclipse, expect the drop you wanted to take longer.
how often it happens
Rain cannot be summoned by any item. Outside Journey Mode, where the power menu switches it on and off directly, you wait. The per tick odds drift up and down, which works out to somewhere between a 17 and a 24 percent chance of rain on a given day, or about one storm every 4 to 6 in-game days. In real time that is a wait of roughly 1 hour 40 minutes to 2 hours 20 minutes. A newly generated world pins the chance at the bottom of that range for the first few minutes before it starts moving.
There is one lever. Killing a Ladybug or a Gold Ladybug, or using either as bait, raises the per tick chance for 30 seconds, and doing it repeatedly stacks that window out to 5 minutes. The effect is real but small, and killing ladybugs also drops your luck, so it is a poor trade unless you were going to lose the luck anyway.
when rain turns into something worse
If the wind climbs while regular or heavy rain is falling, the two combine into a Thunderstorm and lightning starts hitting the surface. There is no announcement, so a calm fishing trip can become dangerous while you are watching a bobber. Glance at the wind reading on a Weather Radio when the sky gets loud, and get a solid roof over yourself if it has.
One small note for anyone testing things: the rain effect a Rain Cloud produces is decoration and has nothing to do with the weather event. It will not bloom a Waterleaf and it will not help your fishing power.