Learn German: Du wohnst in Deutschland.

Because we are using the informal "you" (du). When talking to a single friend, family member, or child, you use du and add the ending -st to the verb. The dictionary form is wohnen (to live), so you take off the -en and add -st to get wohnst.

How would I say this if I were talking to someone I need to be formal with?

You would use the formal "you" (Sie). The sentence would become Sie wohnen in Deutschland. Notice that with Sie, the verb uses the -en ending, which is usually exactly the same as the dictionary form of the verb.

Why isn't there a word for "the" before Deutschland?

In German, most countries do not use an article (like "the") when you say you live in them. Just like in English, you simply say in Deutschland (in Germany), not "in the Germany".

How do you pronounce the "-st" at the end of wohnst?

It sounds just like the English "st" in "stop". While an "s" before a "t" at the very beginning of a German word often makes a "sh" sound (like in Stadt), it makes a normal "s" sound when it is a grammatical ending added to a verb.