I just downloaded Python 3.8.0 and built (from source) on Ubuntu 18.04. I used these options to configure:

  ./configure --enable-shared --enable-ipv6 --enable-optimizations

The shared library gets installed into /usr/local/lib:

  find / -type f -name libpython3.8.so.1.0
  /usr/local/src/Python-3.8.0/libpython3.8.so.1.0
  /usr/local/lib/libpython3.8.so.1.0
  
/usr/local/lib is defined as a path to search for shared libraries: 

  # /etc/ld.so.conf loads all /etc/ld.so.conf.d/*.conf
  grep /usr/local  /etc/ld.so.conf.d/*.conf
  /etc/ld.so.conf.d/i386-linux-gnu.conf:/usr/local/lib/i386-linux-gnu
  /etc/ld.so.conf.d/i386-linux-gnu.conf:/usr/local/lib/i686-linux-gnu
  /etc/ld.so.conf.d/libc.conf:/usr/local/lib
  /etc/ld.so.conf.d/x86_64-linux-gnu.conf:/usr/local/lib/x86_64-linux-gnu

But, the python executable is unable to find it:
  /usr/local/bin/python3.8
  /usr/local/bin/python3.8: error while loading shared libraries: 
    libpython3.8.so.1.0: cannot open shared object file: No such file
    or directory