Clear
Basically no weather. The only condition where your health regenerates as you walk around.
Rainy
Moves: Drizzle or Rain Dance. Lessens the power of fire moves by 50%. Makes water type moves more effective by 50%. Thunder and Hurricane will gain 100% accuracy. It also lessens the power of Synthesis and Moonlight by 3/4, and makes Solar Beam charge for one more turn.
Sunny
Moves: Drought or Sunny Day. Increases the power of fire moves by 50% and decreases the effectiveness of water moves by 50%. The accuracy of Thunder and Hurricane are reduced to 50%. Synthesis and Moonlight have a 2/3 recovery. Solar Beamneeds no charge.
Sandstorm
Moves: Sand Stream or Sandstorm. Boosts the Sp. Def. of Rock-type Pokémon by 50%. All Pokémon who are not Ground, Rock, or Steel type will take periodic damage. Synthesis and Moonlight are lowered to 1/4 recovery, and Solar Beam charges an extra turn.
Hail
Moves: Snow Warning or Hail. This weather periodically damages all Pokémon except Ice type and Blizzard will hit with 100% accuracy.
Snowy
Ice types get an extra turn and HP will not regenerate.
Intensely Sunny
Moves: Primal Groudon's ability in Desolate Land. Water moves do no damage.
Oppressively Rainy
Moves: Initiated by Primal Kyogre's ability in Primordial Sea. Fire moves do no damage.
Strong Winds
Moves: Mega Rayquaza's Delta Stream ability. Causes a decrease in the weaknesses of flying types.