How do I work with the Mac built-in spelling system?

You're right, that's a Mac 101 sort of question, but we all started out somewhere and there's no shame in learning. At least you're asking, not just ignoring it or getting frustrated! (well, you might be getting frustrated but that's another story)

The red squiggly line that shows up under words is indeed the result of the Mac's built-in spelling subsystem highlighting words that it believes you have misspelled. Sometimes it's right, and other times, well, it can get confused about names and slang, not to mention it doesn't like obscenities either.

Generally, when you see a squiggle underline, it's something you should Control-click on. Ahh, the lightbulb goes off.

Let me step you through a couple of interesting features about this. First off, in Apple Mail, here's what I see when I have a misspelling:

You can see that I have misspelled "communicate". Now, when I Control-Click on it:

Look at all those options! Generally, I just pay attention to the very top of the contextual menu that pops up, showing its suggestions for correct spelling. Choose the correct spelling (in this case "communicate") and it'll instantly fix it in your message.

Note here that you can teach the spelling system that the word it's highlighted is indeed properly spelled if it's jargon, slang, a name or another word that you know isn't in error and don't want to see flagged again in future email messages. Choose "Learn Spelling". Rather just have the spelling system ignore the word in this message? Chose "Ignore Spelling" instead.

If you want to tweak the settings so that you don't see these red squiggly underlines, simply go down a little bit to "Spelling and Grammar" and you'll find:

Move out one more by choosing "Check Spelling" and:

Now you can see how to disable this, though I don't recommend it personally. I know that spell check is a major contributor to my coming across well in email messages! :-)

Btw, you should also try Control-Clicking on a word that isn't misspelled. Here's what I see when I fix "communicate" and then ctrl-click on it:

One thing I find useful if I'm using a word where I'm not 100% sure I'm using it correctly is to select "Look Up In Dictionary". Here's what it tells me about this particular word:

Surprisingly detailed and it's a free part of Mac OS X. What's not to love about that?