ROOT is a framework based on C++ that is specialized in processing data in High Energy Physics. Some of its central classes are

• TTree to store data; typically variables are stored in branches for each entry/event (e.g. a proton-proton collision),
• TH1 to make histograms,
• TLorentzVector to make a four-vectors that you can boost, or add together with simply +,
• TBrowser to browse ROOT files containing trees, histograms, …

Once installed, you can use its extensive libraries in your C++ code or in the ROOT command line. If you don't like C++ or pointers, it is also possible to use ROOT in python, a.k.a. pyROOT. This is definitely a good choice for doing simple things, such as making plots.

Always keep the the reference manual (a.k.a. class index) handy: it lists all the available classes and their methods, sometimes even examples.

Helpful materials to get started:

• ROOT tutorial by Dr. Seligman is very nice; it covers the all basics of ROOT in both C++ and python and teaches how to use the reference manual to solve problems by yourself.
• These introductory slides to ROOT also covers ROOT in both C++ and python, and is shorter. It uses these files.
• The official ROOT examples and tutorials (which should also be available on your machine in $ROOTSYS/tutorials/ after installation of root).
• The official ROOT reference manual (a.k.a. class index) lists all available classes and their methods, which is really useful to keep handy.
• The official ROOT user guide (index of older versions).
• Some useful pyROOT examples:
  • handling TTree trees,
  • handling TH1 histograms,
  • handling TFile files and TDirectory directories,
  • RooFit and RooStats tutorials.
• More on fitting in ROOT.
• Some useful and advanced examples made by the LHCb group.