The Esrog should be wrapped in flax or kept in foam in a special box (or the box it was shipped in), in a cool dry place. DO NOT REFRIGERATE. One should avoid over-handling the Esrog as this will cause brown discolorations to appear (this does not affect the kashrus of the Esrog). If the Esrog comes with a pitum, it should be handled very carefully as to not break the pitum. Should the pitum fall off, the Esrog is no longer kosher to use for the mitzvah.
The lulav should be stored in it‘s holder in a cool dry place. DO NOT REFRIGERATE. Care should be taken to avoid banging the tip of the lulav against the wall or ceiling, as not to split the center leaf.
Hadassim & Aravos
The Hadassim and Aravos should be placed in a cool place or the refrigerator. When inserting the Hadassim and Aravos in the special "Y" shaped holder, care should be taken not to tear too many leaves. Please refer to "Instructions" for how to set up the Lulav & Esrog.
You may dispose of a lulav in any way that is not degrading. So, you may drop it into a field or put it on a lawn--unless animals might eat it or step on it or if it will be subject to poor treatment before it decays. Don't dispose of a lulav or etrog directly into the garbage. Burn, bury, or wrap them in a bag or one layer of plastic and you may throw it into normal garbage.