Learn Russian: Эта справка нужна для работы.

Нужна is a short adjective used when you need a physical thing or a noun. It changes to match the noun's gender, so we use the feminine нужна to match the feminine noun справка. Надо is used when you need to do an action (a verb), like saying you need to go to work.

Why does the word for work change to работы?

The preposition для (for) always makes the next noun take the genitive case. For regular feminine nouns ending in -а like работа, the genitive ending changes to -ы, making it работы.

Is there no verb in this sentence?

Exactly! Russian drops the verb to be (is, am, are) in the present tense. You just put the subject and the adjective together to mean 'This certificate is needed'. If you wanted to say it was needed in the past, you would add the past tense verb была right before нужна.

What exactly is a справка?

Справка is a very common Russian word for an official piece of paper that proves a fact. Depending on the situation, it can be a doctor's sick note, a background check, or a general certificate from an employer or university.