I started writing assembly in 1977 by taking the long route: first learning basic operations (and, or, xor, not) and octal math before writing programs for the DEC PDP-8/E with OS/8 and 8k of memory. This was in 1977.
Since then I have discovered a few tricks on how to learn assembly for architectures I am unfamiliar with. It's been a few: 8080/8085/Z80, x86, 68000, VAX, 360, HC12, PowerPC and V850. I seldom write stand-alone programs, it's usually functions that are linked with the rest of the system which is usually written in C.
So first of all I must be able to interface to the rest of the software which requires learning the parameter passing, stack layout, creating the stack frame, parameter positions, local variable positions, discarding the stack frame, returned values, return and stack cleanup. The best way to do this is to write a function that calls another function in C and examine the code listing generated by the compiler.
To learn the assembly language itself I write some simple code, seeing what the compiler generates and single-stepping through it in a raw debugger. I have the instruction set manuals close by so I can look up instructions I am unsure of.
A good thing to get to know (in addition to the stack handling mentioned previously) is how the compiler generates machine code given a certain high-level language construct. One such sequence is how indexed arrays/structures are translated into pointers. Another is the basic machine code sequence for loops.
So what is a "raw debugger?" To me it's a debugger that is part of a simple development package and that doesn't try to protect me from the hardware like the Visual debugger(s). In it I can easily switch between source and assembly debugging. It also starts quickly from inside the development IDE. It doesn't have three thousand features, more likely thirty and those will be the ones you use 99.9% of the time. The development package will typically be part of an installer where you click once for license approval, once for approving the default setup (don't you love it when someone has thought about and done that work for you?) and a last time for install.
I have one favorite simple development environment for x86-32 (IA-32) and that is OpenWatcom. You can find it at openwatcom.org.
I am fairly new to x86-64 (AMD64) but the transition seems straightforward (much like when moving from x86-16 to x86-32) with some extra gimmicks such as the extra registers r8 to r15 and that the main registers are 64 bits wide. I just recently ran across a development environment for XP/64, Vista/64 and 7/64 (probably works for the server OS:s as well) and it is called Pelles C (pellesc.org). It is written and maintained by one Pelle Orinius in Sweden and from the few hours I've spent with I can say that it is destined to become my favorite for x86-64. I've tried the Visual Express packages (they install so much junk - do you know how many uninstalls you need to do afterwards? more than 20) and also tried to get gcc from one place to work with an IDE (eclipse or something else) from another.
Once you've come this far and you come across a new architecture you will be able to spend an hour or two looking at the generated listing and after that pretty much know what other architecture it resembles. If the index and loop constructs appear strange you can look over the source code generating them and perhaps also the compiler optimization level.
I think I should warn you that once you get the hang of it you will notice that at desks close by, at the coffee machine, in meetings, in fora and lots of other places there will be individuals waiting to scorn you, make fun of you, throw incomplete quotes at you and give uninformed/incompetent advice because of your interest in assembly. Why they do this I don't know. Perhaps they themselves are failed assembly programmers, perhaps they only know OO (C++, C# and Java) and simply don't have a clue as to what assembler is about. Perhaps someone they "know" (or whom a friend of theirs knows) who is "really good" may have read something in a forum or heard something at a conference and therefore can deliver an absolute truth as to why assembly is a complete waste of time. There are plenty of them here at stackoverflow.
