What is the best way to make the transition from Microsoft Word to LaTeX?

The best way to learn it is simply to do it. Find someone else's template (e.g. from a friend) to get started. From there on you can always tinker and experiment with it to gain a greater insight.

http://wikibooks.org/wiki/LaTeX is a pretty good reference.

If you're in college/university there are probably a lot of people who can help you (particularly in science, math, CS and similar programs). At my university, the department of mathematics usually have beginner's LaTeX courses at the beginning of the year to get people started.

Also, often when people are editing text in Word they're focusing on how it looks. Make sure you don't do that when writing LaTeX. Just write it. The parser will figure out how to make it look good.

In addition to the advice in the other answers, I'd say be ready to make changes to how you work. Word (and indeed all word processors) are fundamentally different from LaTeX. Some things that people do in Word are regarded as poor typography, and so are discouraged by many LaTeX users. So the question is not always 'Word can do this, how do I do it in LaTeX?' but 'Should I do this at all, and if so how do I do it in LaTeX?'. It's subtle, I know, but it will also help you get the best from the other answers you were given.

I think that the other answers here are quite good. But, they left out one thing which I think can cause a real problem for those new to LaTeX.

If you've used Word for more than a few minutes, you've likely got into the habit of saving your document quite often. That's a good habit, no matter the program you use to edit with. But, with LaTeX, you also really ought to get into the habit of compiling your document fairly often, too. You can really cut down on frustration that way. It is much easier to locate an error introduced in the last 5 minutes than it is one introduced in the last 5 hours!