I will try but I'm not sure if this is best explanation: However is just like "but" which puts some kind of condition on the beginning of the statement . I had planned to travel to China this summer . However , my mom got sick so I decided not to go. Nevertheless is more like, "eventhough situation A is this way , situation B is still going to be going forward. My mom got sick this summer. Nevertheless, I still plan to to go to China and travel. Studying a foreign language is fun but it takes a lot of hard work Speaking like a native speaker is nearly impossible. Nevertheless, you should continue to make oral fluency your goal I don't think my explanation is full enough. Hopefully, someone with more of a grammar background will help you also.

However is used to start a sentence or clause that contrasts with what you just said. For example "I don't like cheese. However, I do like grilled-cheese sandwiches". Nevertheless is used when saying something in spite of something else. For example "I prefer to eat meat, but nevertheless ate vegetarian food when it was offered to me". It essentially has the same meaning as however. However, however has several more uses. It can both contrast what was just said, but also be used as a substitute for "In whatever way" and "To whatever extent".