The “is” in the “A is B” pattern is not the は in the middle, but the です or だ at the end.

The は just indicates what you are talking about.

The two sentences translate to:
I teach Japanese.
I learn English.

Just to confuse matters, it’s fairly common to drop particles in casual speech, usually starting with the は. You’ll usually find it’s replaced by a comma (or a brief pause, in speaking). But yeah, in polite speech, the は stays. =)

Also, particles modify the word that comes before. That is, を designates the object of the verb, but doesn’t do anything to the verb itself.

この ほん は いくら です か。
この ほん、 いくら の？

I think that’s what Joel is referring to. The first is like “How much is this book?” while the second is like “This book, how much?”.

Yeah, that’s basically it. IME’s being funny on my computer at the moment, otherwise I would have answered sooner. Casual speech tends to leave out all sorts of grammar bits – however, it’s kind of important to know the grammar that’s being left out first, so don’t concentrate too much on being casual until you’ve learnt how it works in the first place. =)

For the fun of it, here’s an example of things being dropped in casual speech: 行かなきゃ is an abbreviation of 行かなければ, which means “if you don’t go”. On its own, it doesn’t make a great deal of sense, but it’s actually a kind of verbal shorthand for 行かなければならない, which means “you must go” (or literally, “if you don’t go, that’d be bad”). If you forget the grammar it represents, though, and you’re presented with 行かなきゃ, you’ll be left going “Do go? Don’t go? Must go? Musn’t go?”