The 390 is pretty simple, I don't have mine in front of me, but, here goes..
Make certain the gun is unloaded.
Press the small button on the shell lifter, lock bolt to rear.
Unscrew barrel nut, remove forend, barrel, and piston
Grasp operating handle and remove by tugging straight away from the bolt
Grasp the metal action rod sleeve that surrounds the magazine tube and release the bolt ** carefully as the bolt wants to fly out the front of the action **
Slide the bolt and carriage from the receiver
The trigger can be removed by pushing the large dimpled retaining pin through the receiver and removing it. Slide the trigger assembly forward approx 1/16" and pull down on the trigger guard to remove the unit.
That is as far as you need to go for a thorough cleaning of the action. Do not disassemble the trigger unit any further.
There are two gas ports inside the gas cylinder that bleed gas from the barrel to operate the piston these can be cleaned by getting a few drops of solvent in there and using a pipe cleaner or torch tip cleaner. For best results clean these ports before and after cleaning the barrel.
The piston/cylinder is really the "dirty" part of the gun, soak the piston in solvent and scrub with a Scotch Brite pad.
I hope that helps!
Jim