Setting up wireshark for non root user

$USER is here to see as a shell variable. The third command above adds your user to the wireshark group and should be replaced by sudo adduser <yourUser> wireshark.
Now you should be able to invoke wireshark as yourself (no need to sudo anymore).

As has been pointed out by Guerlando Ocs you may encounter a situation where the group wireshark doesn't exist. In this case you can resolve the problem by first running

sudo dpkg-reconfigure wireshark-common 

and selecting yes so it creates the group for non root users.

This is how I installed Wireshark and made it work, running it as non-root user:

Install Wireshark:

sudo apt-get update
sudo add-apt-repository ppa:dreibh/ppa
sudo apt-get update
sudo apt-get install wireshark

Enable it to run as non-root user:

sudo dpkg-reconfigure wireshark-common
sudo adduser <yourUser> wireshark
sudo chmod +x /usr/bin/dumpcap