I think a good place to start is to flick through the not so short introduction to LaTeX. Obviously, you don't need to read it cover-to-cover, but it's good to read enough to understand how and more importantly why LaTeX is different from a word processor like Word.
The first most disorienting thing about LaTeX is that you don't have a WYSIWYG approach. (What You See Is What You Get). If you're unfamiliar with the idea of markup this is quite a change. Instead of showing your computer what you want by selecting the text and clicking the "bold" button, LaTeX works by getting you to tell your computer what you want:
\textbf{Something Something Dark Side}
This command \textbf is basically saying to your computer "make the text between braces boldface".
When learning LaTeX, the most important thing is knowing where to go when you get stuck. I've found googling the problem to be a surprisingly good way of finding answers to problems. For example, if you want to know how to turn off automatic numbering of the sections, googling "turn off section numbering LaTeX" brings up two sites with useful information as the first hits: The LaTeX wikibook page on document structure and a blog with some tips and tricks which both include ways to solve the problem.
The LaTeX wikibook is a good resource. It is pretty basic, but it covers the basics rather well. Another LaTeX primer is available here.
If it's a particular package you're having difficulty with, use the texdoc facility. So if you're struggling with, say, the hyperref package, typing texdoc hyperref into the command line will open up the documentation for that package. This works for most packages. (If you're on Windows, I suppose Start Menu > Run gets you a command line, right?)
There is an awful lot to learn, and don't try and learn it all at once. Start with a simple project, get that to work. And only then think about how to complicate matters. LaTeX takes practice. You won't be able to migrate from doing everything in Word to doing everything in LaTeX overnight... But stick at it and you can do pretty much everything Word can and more! And better.
You already know about this site, which is another excellent place to know about. If googling around and the wikibook can't answer your question, someone on this site almost certainly can.
LaTeX is enough if what you want to do is to produce neater documents with fewer errors. TeX is worth knowing if you want to write new programs, macros etc.
LaTeX is about presenting content, while TeX is about formatting. Choose your interest.
Best Answer
The TeXBook (by Knuth himself) is actually great! It starts with examples and explains clearly all the things starting from the simplest things that you're most likely to need, and goes sufficiently deep. It is a strange book in that it needs to be read in multiple passes, but you can do it. It's worth reading, especially since it also gives you insights that can be later crucial — into typography, why Knuth made the choices he made, and other issues about the internals of TeX.