です is the copula – not quite the same thing as the state-of-being verbs. A copula is a verb-like object that goes where no other verb is needed. In English, the copula happens to be the state-of-being verb, which confuses matters a little, but that’s not the case in Japanese.

Anyway, the point is that there’s two basic levels of formality: the polite form, and the dictionary or plain form. (Well, there’s more than two, but for the most part, you’re just going to encounter these two.)

In the polite form, sentences end with です and verbs end with ます. It’s a fairly good neutral level of politeness that will cover pretty much any concievable social situation you’d encounter if you visited Japan as a tourist. Since everything conjugates the same way as well, it makes a fairly good place to start for new learners.

In the plain form, the copula becomes だ or even gets omitted, while verbs have a bunch of different endings all of which have a う-sound – also called the dictionary form, because when you look the words up in a dictionary, that’s what you’re going to find. It’s more casual than the polite form, and there’s also a bunch of grammar structures that require the use of the plain form. It’s a little more complex, but also a bit more versatile.

There’s differing schools of thought as to which form new learners should start with. TextFugu’s elected for polite-form first, while Tae Kim has evidently gone for plain-form first.