There are multiple way on how to determine whether a specific package is already installed on your system. The first dpkg command will list all currenlty installed packages on your system:
# dpkg -l
From here we can search for a specific package by supplying the package name as an argument:
# dpkg -l hello
Desired=Unknown/Install/Remove/Purge/Hold
| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend
|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
||/ Name              Version       Architecture  Description
+++-=================-=============-=============-========================================
ii  hello             2.9-2+deb8u1  amd64         example package based on GNU hello
From the above dpkg's command output we can conclude that hello package is currently installed our system. In case that the about dpkg output would not produce any output means that the package hello is not installed. In the situation that we do not exactly know the name of the package we are searching for we can use meta characters to match possible name.
# dpkg -l 'h*'
Desired=Unknown/Install/Remove/Purge/Hold
| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend
|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
||/ Name              Version       Architecture  Description
+++-=================-=============-=============-========================================
ii  hello             2.9-2+deb8u1  amd64         example package based on GNU hello
un  hello-debhelper                   (no description available)
un  hello-traditional                 (no description available)
un  hoogle                            (no description available)
un  hostapd                           (no description available)
ii  hostname          3.15          amd64         utility to set/show the host name or dom
un  hurd                              (no description available)
However, in this case we also list uninstalled un packages. To list only installed package we can pipe the output to grep:
# dpkg -l 'h*' | grep ^ii
ii  hello             2.9-2+deb8u1 amd64        example package based on GNU hello
ii  hostname          3.15         amd64        utility to set/show the host name or domain name
Another alternative to the above dpkg command is to use the -s status option. For example:
# dpkg -s hello