At the beginning of a conversation with a native speaker, it’s not always apparent to them that you are a learner. If your pronunciation is good, then they may not know from the basic greetings that you won’t understand what they have to say next. So, if they launch into something that’s too long or too complicated for you to process, ask them to repeat it.
This way, they will probably rephrase or repeat more slowly so you will have more time to process what they said and formulate your answer. I often have that ‘ohhh’ moment right after I’ve asked people to repeat themselves (I guess my brain just needs that extra couple of seconds to think things through), but by then I can start thinking about how I am going to reply.
Learn a polite way to ask people to repeat what they said (such as the equivalent of pardon?), or even ask them to speak a little more slowly. People tend to appreciate your effort, and you will get better results than if you try to make them speak in English or another language. You might even get better service or information!