Learn Icelandic: Við forritum og reiknum.

They are present tense verbs conjugated to match the subject við (we). In Icelandic, almost every verb ends in -um when used with við. The dictionary forms (infinitives) are forrita (to program) and reikna (to calculate).

How would I apply this lesson's grammar to say "We know how to program and calculate"?

You would say Við kunnum að forrita og reikna. You conjugate kunna to match "we" (kunnum), add the word að (to), and change the main verbs back to their base infinitive forms (forrita and reikna).

If I change this sentence to use kunna að, do I need to put að in front of both verbs?

No, you don't need to repeat it. Just like in English where we often say "to program and calculate" rather than "to program and to calculate", Icelandic shares the single að across both verbs when they are connected by og.

Does the double rr in forritum change how it is pronounced?

Yes! A double rr in Icelandic is pronounced as a longer, stronger trilled "r" sound compared to the shorter tap of a single r. You will want to clearly roll that double rr.