To get the plasma rifle on Doom II map The Abandoned Mines:

When you begin this level you'll first appear in a small
raised chamber near the center of the map, and you'll be
facing north.  From this starting point, turn around and
Activate the secret panel in this chamber's south wall.

Step through the new opening and follow the raised walkway
until you see an opening in the bars to your right, and
another opening to your left.  If you look left (east)
you'll see a plasma rifle sitting on a tall pillar nearby.

To get it, first turn around on the walkway to face the
opposite (west-side) opening.  Step through, and you'll
drop down into a large, dark, slime-covered room.
Immediately turn left (south), and Run onto the teleporter
pad you'll see a few steps ahead of you in the slime.

You'll appear on top of another pillar, located just north
and east of the pillar where the plasma rifle sits.  Turn
to face that pillar, and Run to jump to the plasma rifle.

If you have the plasma rifle and you're still on its
pillar, simply turn right (west), and Run from the top of
the pillar to land back on the raised walkway.
Or, if you fall off the plasma-rifle pillar to land in the
slime, look left (east) for another teleport pad a few
steps away, and Run onto it.  You'll then appear on top of
another pillar to the south (where a cell pack sits), and
you'll be facing an opening in the bars to the north, where
you can jump back to the walkway again.

PC Doom II players can access a demo for this level showing
how to get to the plasma rifle, by clicking here.