My suggestion is to act with the best assembler producer out there: gcc.
Write simple programs in C and then compile them with the -S switch. you will get a file.s containing the assembler code. Tinker with it and you will learn it.
The best part is that if you want to learn a different assembler, you can just compile gcc as cross compiler, and produce assembler for any supported platform.
Remember to disable optimizations with -O0, otherwise you could find strange tricks.
This is hello world in assembler
    .cstring
LC0:
    .ascii "hello world!\0"
    .text
.globl _main
_main:
    pushl   %ebp
    movl    %esp, %ebp
    pushl   %ebx
    subl    $20, %esp
    call    L3
"L00000000001$pb":
L3:
    popl    %ebx
    leal    LC0-"L00000000001$pb"(%ebx), %eax
    movl    %eax, (%esp)
    call    L_puts$stub
    movl    $0, %eax
    addl    $20, %esp
    popl    %ebx
    leave
    ret
    .section __IMPORT,__jump_table,symbol_stubs,self_modifying_code+pure_instructions,5
L_puts$stub:
    .indirect_symbol _puts
    hlt ; hlt ; hlt ; hlt ; hlt
    .subsections_via_symbols