Learn German: Weder ist das Hemd kariert, noch ist es gestreift. - Neither is the shirt checkered, nor is it striped.

In this sentence, weder and noch both occupy the first position of their respective clauses. Because German requires the conjugated verb to be in the second position, the verb (ist) comes before the subjects (das Hemd and es). This swapping of the subject and verb is called inversion.

Can I start the sentence with Das Hemd instead of Weder?

Yes! If you start with the subject, the verb still takes the second position: Das Hemd ist weder kariert... However, the second clause usually remains the same (...noch ist es gestreift), because noch sits at the beginning of that clause and keeps the verb in the second position.

Do I need to add nicht to make the sentence negative?

No, the conjunction pair weder ... noch already means neither ... nor. Just like in English, adding an extra negative word like nicht is unnecessary and would make the sentence grammatically incorrect.

Are kariert and gestreift adjectives or verbs here?

They are acting as adjectives to describe the shirt. They look like past tense verbs because they are past participles (from the verbs karieren and streifen) that have been turned into adjectives. This is very common in German, just like striped and checkered in English!