How to print a number in assembly NASM?

If you're already on Linux, there's no need to do the conversion yourself. Just use printf instead:

;
; assemble and link with:
; nasm -f elf printf-test.asm && gcc -m32 -o printf-test printf-test.o
;
section .text
global main
extern printf

main:

  mov eax, 0xDEADBEEF
  push eax
  push message
  call printf
  add esp, 8
  ret

message db "Register = %08X", 10, 0

Note that printf uses the cdecl calling convention so we need to restore the stack pointer afterwards, i.e. add 4 bytes per parameter passed to the function.

You have to convert it in a string; if you're talking about hex numbers it's pretty easy. Any number can be represented this way:

0xa31f = 0xf * 16^0 + 0x1 * 16^1 + 3 * 16^2 + 0xa * 16^3

So when you have this number you have to split it like I've shown then convert every "section" to its ASCII equivalent.
Getting the four parts is easily done with some bit magic, in particular with a right shift to move the part we're interested in in the first four bits then AND the result with 0xf to isolate it from the rest. Here's what I mean (soppose we want to take the 3):

0xa31f -> shift right by 8 = 0x00a3 -> AND with 0xf = 0x0003

Now that we have a single number we have to convert it into its ASCII value. If the number is smaller or equal than 9 we can just add 0's ASCII value (0x30), if it's greater than 9 we have to use a's ASCII value (0x61).
Here it is, now we just have to code it:

    mov si, ???         ; si points to the target buffer
    mov ax, 0a31fh      ; ax contains the number we want to convert
    mov bx, ax          ; store a copy in bx
    xor dx, dx          ; dx will contain the result
    mov cx, 3           ; cx's our counter

convert_loop:
    mov ax, bx          ; load the number into ax
    and ax, 0fh         ; we want the first 4 bits
    cmp ax, 9h          ; check what we should add
    ja  greater_than_9
    add ax, 30h         ; 0x30 ('0')
    jmp converted

greater_than_9:
    add ax, 61h         ; or 0x61 ('a')

converted:
    xchg    al, ah      ; put a null terminator after it
    mov [si], ax        ; (will be overwritten unless this
    inc si              ; is the last one)

    shr bx, 4           ; get the next part
    dec cx              ; one less to do
    jnz convert_loop

    sub di, 4           ; di still points to the target buffer

PS: I know this is 16 bit code but I still use the old TASM :P

PPS: this is Intel syntax, converting to AT&T syntax isn't difficult though, look here.