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Questions & Answers about Ты знаешь художника?
Why does the word for artist end in -а (художника) if it is the direct object?
Художник (artist) is a masculine noun. Normally, masculine direct objects don't change in the accusative case. But because an artist is a living person (animate), we must add -а. For masculine animate nouns, the accusative case looks exactly like the genitive case!
Why is the verb знаешь instead of just знать?
Знать (to know) is the dictionary form (infinitive). Because the subject of the sentence is ты (the informal you), we have to change the verb to match it by using the -ешь ending.
There is no word for 'Do' in this sentence. How does Russian form 'Do you...' questions?
Russian doesn't use helper words like 'do' or 'does' for questions. You just use the exact same words as the statement Ты знаешь художника (You know the artist) and change your tone of voice to a questioning pitch on the verb, or add a question mark in writing.
What if the object wasn't a person, like asking 'Do you know the museum?'
If the masculine noun is inanimate (not a person or animal), it doesn't change in the accusative case. Museum is музей, so you would just say Ты знаешь музей? without adding an -а.