Step by step

Dress the radicchio segments with some olive oil

Tips
When buying a fresh radicchio it is very important that the leaves are shiny and neither too withered nor too wet, because too much water can cause the loss of vitamin content. Since you keep it in the fridge, and to avoid too much moisture damaging the leaves, keep it in a paper bag. Also, to take away any overly bitter taste, soak it in cold water and then dress with a good balsamic vinegar.
Trivia
The denomination ‘Radicchio Rosso di Treviso’ is a protected term in Italy, meaning that it can be used only for produce made in just over twenty municipalities in the provinces of Treviso, Padua and Venice, identified by the European Union. Thus "Radicchio di Treviso" could not be used for something produced in, for example, Belluno: the improper use of the name would be subject to a legal penalty.