Nasm Asembly help?

I'm having some problems figuring out how to program in x86_64 assembly.  None of the classes I've taken on assembly have ever trained me on modern assembly programming, and I figured it would make me reach satori, so I would like to learn it.  I found this code online, and I was trying to get it to work on my ubuntu system.

   1.
      global _start
   2.
      
   3.
      section .data
   4.
      hello db "Hello, World!", 10
   5.
      length equ $-hello
   6.
      
   7.
      section .text
   8.
      
   9.
      _start:
  10.
      mov eax, 4 ; write to file
  11.
      mov ebx, 1 ; STDOUT handle
  12.
      mov ecx, hello ; our message
  13.
      mov edx, length ; size of message
  14.
      int 80h ; execute the syscall
  15.
      
  16.
      xor ebx, ebx ; send 0 as 'exit code'
  17.
      mov eax, 1 ; terminate process
  18.
      int 80h ; execute the syscall

When I was linking the object code it gave me an error about how it isn't compatible with my architecture.  What is so different about i386 and i386_64 programming?

OP why don't you just decompile (objdump -d) a C program that does the same and look at the output?

Also, you should look at the x86_64 ABI (which has important differences from the traditional x86 one). Take that into account.