Learn Arabic (Modern Standard): هو طالب مجتهد.

In Arabic, adjectives always come after the noun they describe. So instead of saying 'a hardworking student', you literally say 'a student hardworking' (طالب مجتهد).

There's no word for 'a' here. How do we know it means 'a hardworking student'?

Arabic doesn't have a word for 'a' or 'an'. Instead, you show a noun is indefinite by leaving off the prefix for 'the' (الـ). Because both طالب and مجتهد do not have الـ, they match in definiteness, giving us 'a student, a hardworking one'.

How would I change this sentence to say 'She is a hardworking student'?

You would need to change the pronoun to هي (she), and then make the noun and adjective feminine so they agree with her. You do this by adding the feminine ending taa marbuta (ة) to both words. The sentence becomes: هي طالبة مجتهدة.

Where is the word for 'is' in this sentence?

Arabic sentences don't use a word for 'is' or 'are' in the present tense. You simply put the subject (هو, meaning 'he') right next to the information about him (طالب مجتهد) to mean 'He is a hardworking student'.