The primary effect of Rain Dance is to cause all Water-type attacks to do 50% more damage and all Fire-type attacks to do 50% less damage. Fixed damage from those types, such as the damage from Clamp's secondary effects, are unaffected. Other effects of the move include changes to the accuracy of Thunder and the effectiveness of the time-dependent recovery moves.
Rain Dance's effect on Thunder increases its accuracy to 99.6% and causes the attack to ignore other modifications to the Accuracy and Evade stats.
Time-dependent recovery moves (Moonlight, Morning Sun, and Synthesis) will recover half as much as they would otherwise while Rain Dance is in effect.
Rain Dance is a Weather Effect move. Weather Effect moves last for 5 rounds. Weather effect moves do not actually target either pokemon in play. As such, they are not subject to any form of Accuracy modification, including the Evade modifiers of either pokemon, Protect/Detect, or Brightpowder. They also do not directly figure into attacks which take damage dealt to a pokemon by a single attack into account, such as Bide, Counter, or Destiny Bond.
There may only be one Weather Effect move active at one time. If a Weather Effect move other than the one currently active is used, the current one stops and the new one will start its 5 rounds of effect.
Weather Effect moves include: Rain Dance, Sandstorm, and Sunny Day.
*Despite what may be found in the gameboy code and in various guides, Rain Dance's accuracy is 100% (as stated in the Stadium description). It will never miss.