How to create a text editor in assembly language?

There are important errors in your code:

• DL for X and DH for Y. You are not using them correctly in your moveLeft, moveRight, moveUp and moveDown labels.
• Int 16h is better for special keys like arrows.
• You cleared the screen after each key, so the cursor returned to the top left corner every time.

Here is your code improved, tested with EMU8086 (arrows indicate changes):

.model tiny
.code

org 100h

program:    
mov cx, 10
mov ah, 7
int 21h
cmp al, 0 ; start
je clearS ; clear screen

start:  
mov ah, 0      ;<==================================
int 16h        ;<==================================
cmp al, 27 ; ESC
je fin
cmp ax, 4800h  ;<==================================
je moveUp
cmp ax, 4B00h  ;<==================================
je moveLeft
cmp ax, 4D00H  ;<==================================
je moveRight
cmp ax, 5000h  ;<==================================
je moveDown
jmp start      ;<==================================

moveRight:
mov dl, posX
mov dh, posY     ;<==================================
inc dl ; posX ++
mov posX, dl
jmp prntCrs
jmp start

moveLeft:
mov dl, posX     ;<==================================
mov dh, posY     ;<==================================
dec dl ; posX -- ;<==================================
mov posX, dl     ;<==================================
jmp prntCrs
jmp start

moveUp: 
mov dl, posX     ;<==================================
mov dh, posY     ;<==================================
dec dh ; posY -- 
mov posY, dh     ;<==================================
jmp prntCrs ; print cursor
jmp start

moveDown:   
mov dl, posX     ;<==================================
mov dh, posY     ;<==================================
inc dh ; posY ++ ;<==================================
mov posY, dh     ;<==================================
jmp prntCrs        
jmp start

prntCrs:      ; print cursor
mov ah, 2h
int 10h

clearS:         ; clear screen
;mov ah, 7      ;<==================================
;mov al, 25     ;<==================================
;mov ch, 0      ;<==================================
;mov cl, 0      ;<==================================
;mov dh, 24     ;<==================================
;mov dl, 79     ;<==================================
;int 10h        ;<==================================
;mov ah, 2      ;<==================================
;mov bh, 0      ;<==================================
;mov dh, 0      ;<==================================
;mov dl, 0      ;<==================================
;int 10h        ;<==================================
jmp start

fin:int 20h 

posX db 1 dup(0) ; dh = posX -> controls row
posY db 1 dup(0) ; dl = posY -> controls column

end program

      

        
        
        
      

    

Edit: it now displays symbols, adds symbols to the matrix, and updates curr_line

and curr_char

. I used colors for fun. It is still necessary that the cursor does not go out of bounds, for example, does not exceed columns 0 and 80. Next is the new code:

.model tiny
.code

org 100h

program:    

    mov  curr_line, offset matrix
    mov  curr_char, 0

start:
;CAPTURE KEY.
    mov  ah, 0
    int  16h  

;EVALUATE KEY.    
    cmp  al, 27          ; ESC
    je   fin
    cmp  ax, 4800h       ; UP.
    je   moveUp
    cmp  ax, 4B00h       ; LEFT.
    je   moveLeft
    cmp  ax, 4D00H       ; RIGHT.
    je   moveRight
    cmp  ax, 5000h       ; DOWN.
    je   moveDown
    cmp  al, 32
    jae  any_char
    jmp  start   

;DISPLAY LETTER, DIGIT OR ANY OTHER ACCEPTABLE CHAR.
any_char:
    mov  ah, 9
    mov  bh, 0
    mov  bl, color                            
    mov  cx, 1           ; how many times display char.
    int  10h             ; display char in al.
;UPDATE CHAR IN MATRIX.    
    mov  si, curr_line   ; si points to the beginning of the line.
    add  si, curr_char   ; si points to the char in the line.
    mov  [ si ], al      ; the char is in the matrix.   

;!!! EXTREMELY IMPORTANT : PREVIOUS BLOCK DISPLAYS ONE
;CHAR, AND NEXT BLOCK MOVES CURSOR TO THE RIGHT. THAT'S
;THE NORMAL BEHAVIOR FOR ALL EDITORS. DO NOT MOVE THESE
;TWO BLOCKS, THEY MUST BE THIS WAY. IF IT NECESSARY
;TO MOVE THEM, ADD A JUMP FROM ONE BLOCK TO THE OTHER.

;RIGHT.
moveRight:
    inc  curr_char       ; update current char.
    mov  dl, posX
    mov  dh, posY
    inc  dl              ; posX ++
    mov  posX, dl
    jmp  prntCrs

;LEFT.
moveLeft:
    dec  curr_char       ; update current char.
    mov  dl, posX
    mov  dh, posY
    dec  dl              ; posX --
    mov  posX, dl
    jmp  prntCrs

;UP.
moveUp: 
    sub  curr_line, 80   ; update current line.
    mov  dl, posX
    mov  dh, posY
    dec  dh              ; posY -- 
    mov  posY, dh
    jmp  prntCrs         ; print cursor

;DOWN.
moveDown:   
    add  curr_line, 80   ; update current line.
    mov  dl, posX
    mov  dh, posY
    inc  dh              ; posY ++
    mov  posY, dh
    jmp  prntCrs        

prntCrs:                 ; print cursor
    mov  ah, 2h
    int  10h
    jmp  start

fin:
    int  20h 

posX      db 1 dup(0)        ; dh = posX -> controls row
posY      db 1 dup(0)        ; dl = posY -> controls column
matrix    db 80*25 dup(' ')  ; 25 lines of 80 chars each.
curr_line dw ?
curr_char dw ?
color     db 2*16+15
;FOR COLORS USE NEXT TABLE:
;http://stackoverflow.com/questions/29460318/how-to-print-colored-string-in-assembly-language/29478158#29478158

end program

      

        
        
        
      

    

The matrix will be needed if you want to save a file or load from a file. Also, the matrix will be useful in the case of an editor with more rows than the screen size, for example, if the matrix has 100 rows (db 80 * 100 matrix), when the user presses a key, the first lines of the editor will disappear, but when the user presses the key , the first rows can be re-mapped from the matrix.