Learn Icelandic: Hann skoðar peysuna núna. - He is looking at the sweater now.

Peysuna is the object of the verb skoðar (looks at), so it needs to be in the accusative case. For the feminine noun peysa (a sweater), the accusative form is peysu. To say the sweater, we add the definite ending -na to get peysuna.

The translation says "is looking", but where is the word for "is"?

Icelandic doesn't have a separate "is doing" (continuous) tense like English does. The single verb skoðar can mean either "looks" or "is looking" depending on what makes sense in the context.

Why use skoðar here instead of sér (sees)?

Skoða means to actively look at, examine, or check something out. Sjá (the dictionary form of sér) just means to see something with your eyes, without necessarily focusing on it. Since he is actively examining the sweater, skoðar is the better fit.

Could I put núna at the beginning of the sentence?

Yes, you can say Núna skoðar hann peysuna. But remember the V2 rule! If you move núna to the front, the verb (skoðar) must still be the second piece of information in the sentence, so the subject (hann) has to swap places and go right after it.