The Rema (OC 494:3) says there is a minhag to put grass in the Shul on Shavuos. The Mishnah Brura (10) adds that we have a minhag to put trees in the Shul since the Mishna (RH 1:2) says that Shavuos is Judgment Day for the fruits of the tree. The Vilna Gaon stopped this minhag because it became a minhag of the goyim and the Torah forbids us to follow their customs. The opinion of the Rivash (SH”uT 158) differs. He holds that any minhag that has a justifiable reason need not be abandoned just because the goyim have adopted it in their service as well.
One should preferably bring branches from trees that don’t bare fruit since there are differing opinions if one is “Oveir” on Ba’al Tashchis if he cuts even a branch and not the whole tree. Aside from being an issur Torah the gemara brings a story of an Amora who cut a fruit tree and his son died. (Piskei Tshuva OC 494). Revach
the minhag is to use flowers not tree branches.
the minhag today is to use flower not trees. Vehaporetz geder . .
It is interesting to note how comments say “The Minhag today is to…” perhaps more appropriately you should say “our Minhag is…”. Minhag Ashkenaz (German) is to use trees even today. K’Hal Adas Jeshurun in Washington Heights decorates the Shul with many trees and flowers. Minhag Yisrael Torah.