To get the keys on level 2, The Terraformer:

(Note: For a video demonstration of the walkthrough below,
click here.)

BLUE KEY
--------

When you first find the blue key, it will be resting on a
short pedestal in the center of the room.  On the back of
the pedestal is a switch.  Activate it, and the pedestal
drops.  When you try to grab the blue key, it disappears.

The blue key will then pop in and out of existence along
the tops of the other pedestals in the corners of the room.
Eventually the key comes to rest on one of them (the final
pedestal is chosen at random).  When this happens, 4 doors
open up along the back of the room, and behind each of
these doors is a switch.  To either side of 3 of these 4
switches are short vertical slabs rising out of the floor.
Go to the one switch where those slabs are missing.

When you activate this switch, the pedestal where the blue
key now rests will drop.  Run (remember your Run button) to
the pedestal before it rises again.

(Note: For a video demonstration of various movement speeds
in Doom 64, click here.)

If the pedestal rises up before you grab the blue key, just
go back to the switch and try again.

If you activate any of the 3 switches that have those slabs
to either side, a section of the ceiling overhead will drop
down briefly and crush you, possibly killing you if your
health is low.

(For a second example video of solving the blue-key puzzle,
click here.)

RED KEY
-------

As you step out of the room where you got the blue key,
follow the right-hand wall continuously and around to the
right until you come to a blue-keyed door.  Step through
into the tunnel, and walk until you come to a gap in the
floor, then drop down into it and turn left.

Follow the path around to the right, and you'll come to a
series of crushers that begin descending from overhead.
Take note of the flashing squares on the floor.  These are
indicators of areas where the player cannot be crushed.

Carefully move through the crushers until you come to the
end of the path, where the red key will appear on a short
pedestal.  Grab it and head back through the crushers until
you get to a teleporter.  Step on and you'll appear back in
the blue-lit tunnel where you came from a few moments ago.

When you materialize in the tunnel, a blue-keyed door will
be nearby on your left and slightly behind you.  Go through
and head right, through a square opening and down the
steps.  Turn left and look for a red-keyed door nearby, and
step through into a medium sized room.  The button there
will activate the Terraformer just outside the room.  While
the Terraformer is active, the red-keyed door remains shut.

YELLOW KEY
----------

Once you have the red key, activate the Terraformer (the
cluster of 4 large pile-drivers).  The Terraformer creates
a large pit in the ground beneath it.  Jump down into the
pit, and enter the subterranean hallway you'll find there.
Go to the far end of the hallway, and you'll see a switch.

Activate the switch to open a passage on your left.  Go
into the passage and up the stairs.  At the top you'll find
a red-keyed door; Open it and enter the small courtyard.
At one end of this oblong courtyard you'll see some windows
that overlook the courtyard.  Below these windows and to
the left is an opening leading inside.  Step inside, and go
up either one of the curving stairways.

At the top of the stairs is the entrance to one corner of a
large squarish room.  On the far side of the room, opposite
the stairs, you'll see yellow key up in a hole in the wall.
Walk up to the key and turn right.  Ahead you'll see a box
against the same wall, with 4 small red lights above it.
On the wall opposite that box (back on the other side of
the room) is a switch.  Activate the switch to lower that
box and reveal a teleporter.

Go step on the teleporter, and you'll reappear in the room
that has the windows that look down into the courtyard.
In this room look for a switch on the wall and Activate it.
This causes the yellow key to drop down to floor level back
in the room you were in a moment ago.

Step on the teleporter to go back to the room, and grab the
yellow key.