Learn Croatian: Novi radnici marljivo rade. - The new workers work diligently.

It is formed from the adjective marljiv (diligent). In Croatian, you can turn many adjectives into adverbs simply by using their neuter singular form. This usually means giving it an -o (or sometimes -e) ending.

Why is the plural of radnik (worker) spelled as radnici instead of 'radniki'?

When a masculine noun ends in -k, that -k changes to -c before the plural ending -i. This is a very common sound change in Croatian that makes words easier to say.

Why does the adjective novi (new) end in -i here?

Novi describes radnici. Because radnici is a masculine plural noun, the adjective has to match it by taking the masculine plural ending, which is -i.

What is the base form of rade (they work)?

The infinitive is raditi (to work). For most verbs ending in -iti, the 'they' form (third-person plural) is made by dropping the -iti and adding -e.