English has one word for "or", Chinese has two. 还是 (háishi) is for questions where the other person has to choose. 或者 (huòzhě) is for statements, when either choice is possible.
A + 还是 + B？
Use 还是 when you ask someone to choose between two things. The sentence is already a question, so don't add 吗 at the end.
A + 或者 + B.
Use 或者 when you are not asking a question but saying that one choice or the other is possible, or that you do one thing or another. The most common mistake is to use 或者 in a choice question: 你喝茶或者咖啡？ should be 你喝茶还是咖啡？
A statement can contain a question, for example after 不知道 (don't know) or 问 (ask). Then the "or" is still 还是, because there is still a choice to be made: "whether... or...".
还是 has one more common use that has nothing to do with "or". Before a verb, with 吧 at the end, it means "we'd better" or "it would be better to", after thinking about the choices.
Practise this grammar point on paper: 19 exercises using only HSK 3 words, with an answer key on a separate page. Free to print and copy for your class.
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