Learn Icelandic: Maðurinn smíðar borð.

Maður means a man, but adding the suffix -inn makes it definite, meaning the man. In Icelandic, the definite article (the word for the) is attached to the end of the noun instead of being a separate word before it.

If this lesson is about kunna (knowing how to), how would we change this sentence to say The man knows how to build a table?

You would conjugate kunna for the man and change smíðar to its infinitive form with að. The sentence becomes Maðurinn kann að smíða borð.

Is the verb smíða used for building anything at all, like a house?

Not exactly. Að smíða is generally used for crafting, manufacturing, or making things by hand, especially out of wood or metal (like furniture, boats, or jewelry). If you are talking about constructing a large building or a house, you would normally use the verb byggja.

What grammatical case is borð (table) in this sentence?

It is in the accusative case because it is the direct object (it is the thing being built). However, because borð is a neuter noun, its accusative form looks exactly the same as its nominative or dictionary form.