Within a standard QGIS installation on Linux, you have the GRASS tools included. Just go to processing -> toolbox and voila, there they are.
However, there are a lot of GRASS plugins that don't come bundled withe the default installation of GRASS within QGIS. To get them, you have to install them from the GRASS GIS Addons repository. This is a pain.
To install from this repository, first go to plugins -> Manage and Install Plugins and search for GRASS. Check to activate. The GRASS window should pop open automatically, but greyed out; you can't do fuck-all with it yet.
You need to create a mapset. Why? I don't know. Whatever. Just do it. Go to Plugins -> GRASS -> New mapset. Choose a directory for GRASS's database, give it a project name, pick an extent (which might as well be the extent of the project you're currently working on, I don't know if that makes a difference or not), and hit the create button. Yay, things are now un-greyed-out.
In the GRASS Modules, you now have one called the GRASS Shell. Click it and you'll get a console. Type g.extension -l and you'll get a list of the extensions available for install in the Addons repository. Scroll up to see if the one you want is in there. If not, I don't know what to tell you.
Now try to install it with g.extension extension=<extension_name>. For example, I want the image cutlines extension, so I type g.extension extension=i.cutlines.
Of course, this probably won't actually work. It'll try to fetch the relevant plugin from the repository, but you'll as likely as not get an error like: svn: E170000: URL 'https://github.com/OSGeo/grass-addons/trunk/grass7/imagery/i.cutlines' doesn't exist. Cool huh? Aren't you glad you chose Free Software instead of paying a predatory monopolist like ESRI?
Fuckin' A. Let's carry on here. This page purports to describe the g.extension command, which should help us figure out how to get this yak shaved nice and smooth.
Turns out you can specify a URL. So let's try (using my example of the cutlines extension) g.extension extension=i.cutlines url="https://github.com/OSGeo/grass-addons/tree/grass7/src/imagery/i.cutlines"
That also fails. The manual suggests you can specify the git branch, which causes the console to complain that branch is an invalid parameter. Awesome!
Ok, so clone the entire Git repo locally, and try the installation from a local directory: g.extension extension=i.cutlines url="/home/ivan/Documents/git/grass-addons/src/imagery/i.cutlines".
That results in a happy message: GRASS_INFO_MESSAGE(111235,1): Installation of <i.cutlines> successfully finished GRASS_INFO_END(111235,1).
Followed by a sad message: GRASS_INFO_WARNING(111236,1): This add-on module will not function until you set the GRASS_ADDON_BASE environment variable (see "g.manual variables") GRASS_INFO_END(111236,1).
WTAF?
Ok, let's dig into that error. Stack Exchange suggests g.gisenv set="GRASS_ADDON_BASE=~/.grass7/addons". That doesn't obviously do anything (the console simply performs a carriage return). However, if you do it, and then run the install command again, it might work. It did, for me, once.
Good luck!