I believe Ubuntu 16.04 comes with PostgreSQL 9.5. Thats good for a start, but it is a matter of time before you have the need of a PostgreSQL 9.6 cluster. For me it was to import a PG backup from Heroku.
The procedure couldn't have been any easier and is described below. If you are interested in upgrading your old cluster to 9.6 afterwards, you may be interested in this.
sudo -s 'echo "deb http://apt.postgresql.org/pub/repos/apt/ xenial-pgdg main" > /etc/apt/sources.list.d/pgdg.list'
wget --quiet -O - https://www.postgresql.org/media/keys/ACCC4CF8.asc | \
sudo apt-key add -
sudo aptitude update
sudo aptitude install postgresql-9.6 postgresql-client-9.6 postgresql-contrib-9.6
dpkg -l | grep postgresql will give us what is installed and will be some thing like this
ii postgresql 9.5+173 all object-relational SQL database (supported version)
ii postgresql-9.5 9.5.5-0ubuntu0.16.04 amd64 object-relational SQL database, version 9.5 server
ii postgresql-9.6 9.6.2-1.pgdg16.04+1 amd64 object-relational SQL database, version 9.6 server
ii postgresql-client-9.5 9.5.5-0ubuntu0.16.04 amd64 front-end programs for PostgreSQL 9.5
ii postgresql-client-9.6 9.6.2-1.pgdg16.04+1 amd64 front-end programs for PostgreSQL 9.6
ii postgresql-client-common 173 all manager for multiple PostgreSQL client versions
ii postgresql-common 173 all PostgreSQL database-cluster manager
ii postgresql-contrib 9.5+173 all additional facilities for PostgreSQL (supported version)
ii postgresql-contrib-9.5 9.5.5-0ubuntu0.16.04 amd64 additional facilities for PostgreSQL
ii postgresql-contrib-9.6 9.6.2-1.pgdg16.04+1 amd64 additional facilities for PostgreSQL
pg_lsclusters, will show that your 9.5 and 9.6 main clusters to be "online".
pg_lsclusters
Ver Cluster Port Status Owner Data directory Log file
9.5 main 5432 online postgres /var/lib/postgresql/9.3/main /var/log/postgresql/postgresql-9.5-main.log
9.6 main 5433 online postgres /var/lib/postgresql/9.5/main /var/log/postgresql/postgresql-9.6-main.log