We have the lulav and etrog because:
The Torah instructs us to hold four species to celebrate Sukkot.
On the first day you shall take the product of the goodly trees, branches of palm trees, boughs of leafy trees, and willows of the brook, and you shall rejoice before the Lord your God seven days. (Lev. 23:40)
The first three are tied together and together are called a lulav. The fourth is the etrog, a sweet smelling citrus fruit grown in Israel. It is held with the lulav and brought both to the synagogue where it is waved as Hallel is recited.
The four species symbolize the agricultural abundance of God’s role in nourishing Israel.
You shake the lulav and etrog North,West,East and south, up and down.
-JA