Upon opening Conqueror, the default game appears:
Two tribes occupy either side of the board. White pieces denote one tribe, black pieces denote the opposing tribe. By default, white always moves first.
The pieces, in increasing order of rank, are:

SWORDSMAN, moves 1 square on diagonals.

ASSASSIN, moves one or two squares on the horizontal and vertical.

ARCHER, moves 1 square in any direction.

MAGICIAN, moves 1 square on horizontal and vertical. Can cast spells
on enemy pieces up to 2 squares, demoting them to lower-ranking pieces.

WARRIOR (mounted bowman), moves 2 squares in any direction.

POWER MAGICIAN, moves 2 squares on horizontal and vertical (similar
to WARRIOR). Can cast spells on enemy pieces up to 2 squares, demoting
them to lower-ranking pieces.

BONDSMAN: mounted bowman having all the movements of the WARRIOR with
extended 3 square range on the horizontal and vertical. This is the
khan's right hand man (the first bondsman), and is the backup leader
of the tribe.

KHAN, is the main leader of the tribe. The piece moves like a WARRIOR
with an extended 3 square range on the horizontal and vertical and diagonal.
To win, a player must capture both the enemy Khan and the Bondsman.

In the above diagram,
The white
archer at square D2, can move to 5 positions (see red arrows). The piece
is blocked in the other directions by the white magician at square E2
and the white archer at square D1.
The white
swordsman at F2 can move to only one square (see green).
The white
assassin at G3 can move to two squares (see purple).
The black
khan at B7 can move to 5 possible squares (see blue arrows). The other
squares like B6 and B5 are blocked by surrounding pieces.
None of the warrior (W) pieces of either side can move because they
are blocked. (Pieces cannot move off the board)

Above, the
white bondsman at square G4, can move to many positions (see purple
arrows). Note the extended 3 square range on the horizontal and vertical.
The white bondsman can capture the black bondsman at D4, but no other
black pieces.
The black
magician at B2 can physically move to any of the red squares, only 1
square in the horizontal and vertical.
The piece can cast spells on the white archer at D2, demoting it to
the next down in rank (a Swordsman), or cast spells on the white knight
at B4, demoting it to an Archer, the next down in rank.
In turn,
the white archer at A1 can capture the black magician (see the green
arrow).
The black
warrior at A6 can move to any of the blue squares, moving 2 squares
in any direction. It can only capture the white warrior at B4.
If a piece is at centre position D5, below, the potential range of moves are:

Archer: (can move to blue squares)
Warrior: (can move to blue and green squares)
Bondsman: (blue + green + yellow)
Khan: (blue + green + yellow + red)

Magicians are advanced pieces which can move according to the following
move table:
Power
magicians are magicians on horses, graced with the same moving
principles as regular magicians except they enjoy the range of mounted
warriors to unoccupied squares.
Low
magicians are magicians that have been demoted to lower caste.
They have the same moving principles as regular magicians except they
can only cast spells up to 1 square, not 2. Magician spells can be extended to the green marked circles (above) by selecting Game..Rules:
The
archer at B5 can capture the white warrior at C5.
The warrior
at C5 can capture the archer.
The white
warrior cannot capture the black warrior at A6, because its path is blocked
by the pieces at B5 and B6.
The white
warrior can capture the black magician at E5. The magician cannot capture
the white warrior because of his innate rule of not being able to kill
enemies, but he can demote the warrior to the next lower in rank (Archer).
The magician
can also demote the assassin at G5 to a swordsman,
casting his xray spell through the bondsman.
The magician
can also demote the white enemy magician at E3 to a lower ranking one
(M-)
that
can only move one square on the horizontal and vertical, thus severely
limiting his spell-casting ability. If it were white's turn to move, the
magician at E3 could similarly cast a spell on E5 and demote him to a
lower ranking piece.
The Assassin
at G5 (which has 2 squares mobility in horizontal or vertical directions)
cannot capture the magician at E5 because it is blocked by F5 by F. He
can capture the archer at H5 and G7 though. He cannot attack the white
Khan at G2 because the Khan is outside his range, but the Khan at G2 can
capture him because he is within his attack range (3 squares on the horizontal,
vertical or diagonal).
The bondsman
at F5 can capture the black warrior at F8 because he has 3 square range
on the horizontal and vertical.
The
black swordsman at D4 can capture the magician at E3, but he cannot capture
mounted pieces like W at C5.