Imply the question, instead of asking it.
Instead of asking where someone is from, say where you’re from: it’s implied that they will eventually tell you where they’re from.
Instead of asking what someone thinks of a new movie, just say: Movie X is coming out soon, or I wonder if Movie X is a good movie. A request for a comment is implied.
Say “I’m bored” to trigger a conversation on “what should we do now?” or say “I want to [insert random action]” so there’s something to start the discussion.
Say “I like Restaurant A” instead of, do you want to eat at restaurant A?
Often, people’s conversations sound like an interview, with questions asked and answers given. This is especially true if you’re just starting to learn the art of conversation. By avoiding explicit questions, the answer can be more open ended, making answering easier and more interesting: they might have something to say that you didn’t think to ask, so if you asked a question, they wouldn’t be able to say that interesting comment because they would instead need to answer your question. This also takes the pressure off the other person because it’s not a direct demand for an answer. It also protects you from the sting of rejection, because an answer isn’t required anyway!