INT 10h AH=03h

Function 03h returns the cursor of page BH as the BIOS data area has it: the row in DH, the column in DL, and in CX the cursor shape set by function 01h, which all pages share. Nothing on the screen changes.

Its everyday job is to remember the position before moving the cursor and to put it back afterwards, or to find out where DOS output has got to, since DOS moves the same cursor:

MOV     AH, 09h
MOV     DX, OFFSET MSG1  ; "abc" without CR LF: the cursor stays on the line
INT     21h
MOV     AH, 03h          ; read the cursor of page 0
MOV     BH, 0
INT     10h              ; DH = row, DL = column, CX = shape
MOV     [COL1], DL
MOV     AH, 09h
MOV     DX, OFFSET MSG2
INT     21h
MOV     DL, [COL1]
ADD     DL, "0"          ; one digit is enough here
MOV     AH, 02h
INT     21h
MOV     AH, 09h
MOV     DX, OFFSET CRLF1
INT     21h
 
COL1    DB      0
MSG1    DB      "abc$"
MSG2    DB      ": the cursor is in column $"
CRLF1   DB      13, 10, "$"

Saving and restoring the position around output somewhere else:

MOV     AH, 03h
MOV     BH, 0
INT     10h
PUSH    DX       ; the position
; ... move the cursor, write a status line ...
POP     DX
MOV     AH, 02h  ; back where it was
MOV     BH, 0
INT     10h

Pitfalls

CX is overwritten even when only the position was wanted, a classic trap when CX holds a loop count. The values come from the data area, so a program that moved the hardware cursor by programming the CRT controller directly is not seen here. In graphics modes the position is still returned; the shape means nothing there.