Learn Icelandic: Ég kann ekki að forrita tölvuna. - I do not know how to program the computer.

In Icelandic, we use kunna for learned skills or knowledge, like speaking a language or programming. We use geta for physical abilities or when something is currently possible. Because programming is a skill you learn, we use kann.

Does kunna always need að before the next verb?

Yes, when kunna means 'to know how to do something', it must be followed by að and the infinitive verb (here, að forrita). This is different from some other helping verbs you have learned, like vilja (want) or ætla (intend), which skip the að.

Where exactly does ekki (not) go in this kind of sentence?

It goes right after the conjugated verb (kann) and before the að + infinitive block. The pattern is: Subject + verb + ekki + að + infinitive.

What is the base word for tölvuna and why is it in this form?

The base word is tölva (computer). Here it becomes tölvuna because it is the direct object of the verb forrita (to program), which puts it in the accusative case. It also has the definite article attached at the end to mean 'the computer' instead of just 'a computer'.