In order for the linux install to work, you need to first install java 8. In a terminal:
sudo add-apt-repository ppa:webupd8team/java
sudo apt-get update
sudo apt-get install oracle-java8-installer
sudo apt-get install oracle-java8-set-default

Note, if the packages cannot be found, try:

sudo apt-get install default-jre

After installing java 8, run the .deb package in package manager, press install and it should install.

On some operating systems, there will be no start menu shortcut, if so navigate to opt -> openpnp and you should find openpnp.sh

To add a launcher shortcut (in Ubuntu) run:

sudo cp /opt/openpnp/OpenPnP.desktop  /usr/share/applications/