Learn Polish: Znam ten adres bardzo dobrze. - I know this address very well.

The verb znać (here conjugated as znam) is used when you are familiar with a noun, like a person, a place, or a thing. In this sentence, you know a specific object: the address. The other verb for knowing, wiedzieć (like wiem), is used for knowing facts, usually followed by a clause starting with words like 'that', 'where', or 'what'.

Is ten adres in the accusative case here? It looks exactly like the dictionary form.

Yes, it is the direct object of the verb znam, so it must be in the accusative case. However, for non-living masculine nouns like adres, the accusative form is completely identical to the basic dictionary form. The pointing word ten (this) also stays the same.

I learned that dobrze means 'good'. Why does it mean 'well' here?

Dobrze is actually an adverb, which means it describes an action. It translates to 'well' because it describes how you perform the action of knowing. The word for 'good' is the adjective dobry, which is used to describe nouns (like 'a good address').

Why isn't there a word for 'I' at the beginning of the sentence?

In Polish, the ending of the verb almost always tells you who is doing the action. The -m ending in znam specifically means 'I know'. You only need to add the pronoun ja (I) if you really want to emphasize it, like saying 'I am the one who knows it'.