org 100h

mov si, 82h
mov ah, 09h
mov dx, si
int 21h
int 20h    

org 100h

;first of all, get the length of commandline params
       xor ax,ax
       mov si,80h
       lodsb
;AL = Count, now check if there are any
    test al,al
    jz   no_params

        xor cx,cx
        mov cl,al

;else display them
      mov si,string+26
      call prints

        lea si, [DS:81h]      ;<----- Notice 81h not 82h
        call prints_cnt
        jmp ok

        no_params:
        mov si,string
        call prints

ok:
        xor ax,ax
        int 16h
        ret

string db 'No parameters specified !',0
       db 'Here are your parameters: ',13,10,0


;
;  Uses count
prints_cnt:
  ;using cl as counter
        push cx
get:
        pop cx
        cmp cl,-1
        je  done_get
        dec cl
        push cx
        lodsb
        mov dl,al
        call printc
        jmp get
done_get:

ret

;
; dl = Character
printc:
        mov ah,02
        int 21h
ret

; SI = string pointer
prints:
A:
        lodsb
        test al,al
        jz  done
        mov dl,al
        call printc

        jmp A
done:

ret

    

org 100h
start:
        mov si, msg
        call lenstr
        mov ah, 40h
        mov bx, 1
        mov dx, si
        int 21h
        int 20h
msg db  'Hello!', 0
lenstr:
        push si
        xor cx, cx
@@:
        lodsb
        cmp al, 0
        jz @f
        inc cx
        jmp @b
@@:
        pop si
        ret
    

org 100h
 mov edx,81h
 movzx ebx,byte[edx-1]
 mov byte[edx+ebx],'$'
 mov ah,9
 int 21h
 int 20h
    

It's not a good idea to use ah=9 to print a user-inputted string, even if you $-terminate it, because the string can itself contain a $ and then it'll get truncated.

org 100h
use16

start:
        xor     bx,bx               ; clear high & low bytes
        mov     bl,[80h]            ; move the length into BX
        mov     byte[82h+bx+1],'$'  ; move '$' right after the argument
        mov     ah,9                ; we want to display string
        mov     dx,82h              ; message to display
        int     21h                 ; display command-line

        ; wait for keypress
        xor     ax,ax
        int     16h
exit:
        int     20h                 ; return to OS
    

org 100h
use16

start:
        xor     bx,bx               ; clear high & low bytes
        mov     bl,[80h]            ; move the length into BX
        mov     byte[82h+bx],0      ; move 0 this time since we are using BIOS interrupt
        mov     si,82h              ; message to display
        call    printString

        ; wait for keypress
        xor     ax,ax
        int     16h
exit:
        int     20h                 ; return to OS

printString:
    .getchar:
        lodsb
        or      al,al
        jz      .finished
        mov     ah,0Eh
        int     10h
        jmp     .getchar
    .finished:
        ret                         ; return
    

Where you see this line: mov byte[82h+bx],0 ; move 0 this time since we are using BIOS interrupt, I removed the 1 because it brought up letters that were not on command-line. I don't know why. If someone could explain that part for both of us, please.

Really, if you want to nul-terminate the string, it should be [81h+bx], since the command line starts at 81h. If you write to [82h+bx], then you'll write the 0 byte after the 0Dh terminator character; if you write to [82h+bx+1] then you'll write it after the 0Dh plus whatever the next character happened to be (probably something left over from a previous command line).

You don't have to null terminate the string at all. Just use 0xd as your terminating character in the printString subroutine.