How can I correct this code?

Do you see something wrong here?

MOV AL, NUM1
MOV AL, NUM2
MOV SOMMA, AL 

And at that point both NUM1 and NUM2 are characters, and not numeric values. So the first thing you need to do is convert each number to its integer equivalent. So change NUM1 and NUM2 to DW type and save them by:

MOV AH, 01H
INT 21H
XOR AH,AH  ; clear AH
SUB AL,'0' ; make it integer
MOV NUM1,AX

Then do the same with NUM2. But when you add them together the total could be greater than 9, so you need to code the algorithm to convert an integer into printable digits. And you could save duplication by using subroutines for capturing the numbers.

[edit]
There are a few issues here

  1  .MODEL SMALL
  2  .STACK 100H .DATA NUM1 DW ?
  3  NUM2 DW ?
  4  DOM1 DB 'digit the number: ',13, 10 , '$'
  5  DOM2 DB 'digit the other one: ',13, 10 , '$'
  6  RIS1 DB 'the sum: ', 13,10, '$'
  7  SOMMA WB ? ; ***** WB should be DW
  8  .CODE
  9  .STARTUP
 10  MOV AX, @DATA
 11  MOV DS, AX
 12  MOV AH, 09H
 13  MOV DX, OFFSET DOM1
 14  INT 21H
 15  MOV AH, 01H  ;
 16  INT 21H      ; ***** You are trying to store a single character into a word
 17  MOV NUM1, AL ;
 18  
 19  MOV AH, 09H
 20  MOV DX, OFFSET DOM2
 21  INT 21H
 22  
 23  MOV AH, 01H  ;
 24  INT 21H      ; ***** same as NUM1 above
 25  MOV NUM2, AL ;
 26  
 27  
 28  MOV AH, 01H  ; ***** these five lines should have replaced lines 15-17
 29  INT 21H
 30  XOR AH,AH  ; clear AH
 31  SUB AL,'0' ; make it integer
 32  MOV NUM1,AX
 33  
 34  MOV AH, 01H  ; ***** and these five should have replaced 23-25
 35  INT 21H
 36  XOR AH,AH  ; clear AH
 37  SUB AL,'0' ; make it integer
 38  MOV NUM2,AX
 39  
 40  
 41  MOV AL, NUM1  ; ***** You are treating a word as a byte
 42  MOV AL, NUM2  ; ***** this overwrites AL
 43  MOV SOMMA, AL ; ***** you are trying to move the last character to the sum
 44  
 45  MOV AH, 09H
 46  MOV DX, OFFSET RIS1
 47  INT 21H
 48  
 49  SUB SOMMA, 30H ; ***** what is this for?
 50  
 51  MOV AH, 09H
 52  MOV DX, OFFSET RIS1
 53  INT 21H
 54   
 55  SUB SOMMA, 30H ; ***** and what is this for?
 56  
 57  
 58  MOV AH,02H
 59  MOV DL, SOMMA
 60  INT 21H
 61  
 62  MOV AH, 40H
 63  INT 21H 
 64  
 65  END

You need to stop coding and write down on paper the steps needed to get this program working. Print the message that asks for a digit, and read the digit from the user. You then convert the digit from a character to a binary integer, and save it in a variable defined as a DW type. Once you have two digits then you should add them together and store the result in the SOMMA variable. But you cannot print a binary value directly so you need to write a function that converts it to its character representation - and that is a good exercise for you to use your assembler skills. So think slowly what you are trying to achieve and try to make your code follow the logical steps.
[edit]

NUM1 DW ?
NUM2 DW ?
SOMMA DW ?