This answer assumes the games in question are Scarlet and Violet, unless otherwise noted. Details between other games may differ from what is shown here.
Harsh Sunlight
- Boosts the amount of HP Synthesis, Moonlight, and Morning Sun heal. 
- Thunder and Hurricane have 50% accuracy. 
- Solar Beam and Solar Blade become one-turn moves. 
- Growth boosts Attack and Special Attack sharply. 
Sandstorm
- Shore Up restores more HP.
Rain 
Snow/Hail
- Permits the use of Aurora Veil. 
- Blizzard gets perfect accuracy. 
- [Diamond and Pearl] Blizzard has a 30% chance to hit through Protect or Detect when used in hail. 
Fog
- [Gen IV] Weather Ball's power doubles. 
- [Gen IV] All moves set to 3/5 their original accuracy. 
- [Legends: Arceus] All moves' accuracy decreased by an unknown amount. 
[Only in games with Desolate Land] Extremely Harsh Sunlight
- Prevents the use of any Water type move. This includes Natural Gift with a "Water" type berry.
[Only in games with Primordial Sea] Heavy Rain
- Prevents the use of any Fire type move. This includes Natural Gift with a "Fire" type berry.
[Only in games with Delta Stream] Strong Winds
- Forces moves that are super effective against Flying types to deal neutral damage.
[Pokemon XD: Gale of Darkness] Shadowy Aura
- Weather Ball's power doubles and becomes a typeless move.
Snow/Hail, Sandstorm, Rain (and Gen IV Fog)
- Morning Sun, Synthesis, and Moonlight restore less HP. 
- Solar Beam and Solar Blade have their power halved. 
Harsh Sunlight, Sandstorm, Rain, and Snow (Hail) 
- Weather Ball's power doubles and changes to a different type depending on the active weather.
[Only in games with Desolate Land, Primordial Sea, and Delta Stream] Extremely Harsh Sunlight and Heavy Rain
- A Pokemon afflicted by Powder that attempts to use Sunny Day will take damage.
[Only in games with Desolate Land, Primordial Sea, and Delta Stream] Extremely Harsh Sunlight, Heavy Rain, and Strong Winds
- Prevents the use of Sunny Day, Rain Dance, Sandstorm, and Hail.
Weather (Bulbapedia)
Electric Terrain
Grassy Terrain 
- Halves damage taken from Bulldoze, Earthquake, and Magnitude. 
- Grassy Glide has increased priority. 
- Floral Healing restores more HP. 
Misty Terrain
- Grounded Pokemon take half damage from Dragon moves. 
- Misty Explosion's power increases by 50%. 
- Grounded Pokemon can't be affected by non-volatile status conditions. 
- Grounded Pokemon can't be afflicted with confusion. 
Psychic Terrain 
All terrains
- Terrain Pulse doubles power and changes type based on active Terrain. 
- Steel Roller only works when a Terrain is active. 
- Nature Power turns into a different move depending on the Terrain. 
- Secret Power's effects differ based on the active Terrain. 
- Camouflage changes the user's type based on the active Terrain. 
- Defog, Splintered Stormshards, and G-Max Wind Rage clear the active Terrain. 
Terrain (Bulbapedia)