With the US Basic Blastoise's Rain Dance, do you search your deck for
energy, discard pile, or do you just amke a mental note that those pokémon
have __ water energy on them?  I'm very confused about this.
         -AlyKat

Nope.  Rain Dance lets you play unlimited water energy from your hand.  It states nothing about searching your deck or discard pile.  If you have no water energy in your hand, then you can not play any.

Scott