Learn Icelandic: Sækið verkefnið!

The -ið ending tells us this is a plural command, meaning it is directed at two or more people (like "you all, fetch!"). If you were commanding just one person, you would use the singular form, which drops the ending and is just sæk.

The dictionary form of the verb is sækja. Where did the j go in Sækið?

For verbs that end in -ja, the j usually drops out when we add a suffix that starts with a vowel, like the plural command ending -ið. So, we take the stem sæk-, drop the j, and add -ið to get sækið.

Why is the word for "the assignment" written as verkefnið instead of adding the full -ið ending for "the"?

The base word for "assignment" or "project" is verkefni. Because the word already ends in a vowel (i), we just attach a -ð to the end to mean "the". If we added the full -ið, we'd end up with a double vowel, which Icelandic avoids here.

Why doesn't the ending of verkefnið change if it's the object being fetched?

It actually is in the accusative (object) case here! However, because verkefni is a neuter noun, its accusative form looks exactly the same as its nominative (subject) form. Many neuter nouns in Icelandic share this handy shortcut.