Grenade launchers generally tend to have shorter barrels and lower barrel pressures, so it is possible to eliminate the butt stock of a shoulder fired grenade launcher and attach the rest of the parts to the underside of a rifle barrel.
Public domain image of an M4 fitted with an under barrel M203 grenade launcher
In the image above, we have a M203 grenade launcher attached underneath the barrel of an M4 assault rifle. Note that the grenade launcher has its own trigger which is located in front of the M4's magazine. It also has its own adjustable leaf sight, which is the long thin rod in front of the telescopic sight. The leaf sight is used in conjunction with the M4's front sight to launch grenades.
Public domain image of a US soldier using a M203 under barrel grenade launcher attached to the underneath of a M16 assault rifle.
Note how the soldier is using the leaf sight along with the M16's front sight to aim the launcher.
Western made under barrel grenade launchers typically are loaded from the back and the launcher tube either pivots to one side or slides forward to allow the user to load a new grenade cartridge. Russian made grenade launchers are usually loaded from the muzzle.
To launch the grenade, the user typically shifts their hand that is on the rifle's pistol grip to the magazine and then pulls the grenade launcher's trigger. To go back to shooting the rifle, the user simply moves his/her hand back to the pistol grip.
Since the butt stock is shared between the rifle and grenade launcher, this design is much lighter than carrying a rifle and a separate shoulder fired grenade launcher. Unlike rifle fired grenade launchers, the user can walk around with a magazine loaded in the rifle and a grenade cartridge loaded in the launcher and use either at a moment's notice. The user can also easily switch between the two as needed. There are a few disadvantages with this type of launcher though. The first is that the attached grenade launcher alters the balance of the rifle. The second is that these usually don't have as much range as a rifle grenade launcher or a shoulder fired grenade launcher. The third is that these are single shot devices and the user needs to manually reload after each cartridge is fired.
Models such as the US made M203, the German AG36 and the Russian GP-25 and GP-30 are some common under barrel grenade launchers used around the world.