Learn Russian: Твой друг был программистом?

When you state someone's profession using the past tense verb был (was) or the verb стать (to become), the profession needs to be in the Instrumental case. Because программист is a masculine noun ending in a hard consonant, we add -ом to make it программистом.

Can I just say Твой друг был программист using the Nominative case?

Yes, you will sometimes hear native speakers use the Nominative case for professions in casual speech. However, using the Instrumental case (был программистом) is the standard grammatical rule and sounds much more natural in most situations.

How would this sentence change if we were talking about a female friend?

The pronoun, noun, and verb all need to change to feminine: Твоя подруга была... For the profession, you have two choices: you can use the feminine form in the Instrumental case (программисткой) or keep the official masculine title but still put it in the Instrumental (программистом).

How do I know this is a question if there is no question word?

Russian yes/no questions don't require helper words like "Did" or "Was" at the beginning. You just use the standard word order and raise your vocal pitch on the word you are emphasizing, usually the verb был or the profession программистом.