In order to get PyROOT working for Python 3, you must build ROOT with a flag that specifies Python 3 in the installation.  This method will create a folder titled root-6.16.00 in your current directory, so organize things how you see fit. Then the steps are relatively simple:

wget https://root.cern/download/root_v6.16.00.source.tar.gz
tar -zxf root_v6.16.00.source.tar.gz
cd root-6.16.00
mkdir obj
cd obj
cmake .. -Dminuit2=On -Dpython3=On
make -j8

If you wish to do a different version of ROOT, the steps should be the same:

wget https://root.cern/download/root_v<version>.source.tar.gz
tar -zxf root_v<version>.source.tar.gz
cd root-<version>
mkdir obj
cd obj
cmake .. -Dminuit2=On -Dpython3=On
make -j8