Hi Ludvig,
and welcome to the ROOT forum!
Your ROOT file contains a TTree. You need to open it using ROOT! With a working ROOT installation, you can use rootbrowse <filename.root> to open a GUI that lets you inspect the file. To actually process it, there are a number of interfaces, see e.g. this answer for a list of the most common ones in C++. If you are using python, ROOT comes with dynamic python bindings that let you access almost all of the C++ classes and functions from python. There are a number of tutorials and a ROOT primer.
Do not hesitate to ask more specific questions in this thread.
Cheers,
Enrico