I can't pick up and elephant with my bare hands, and neither can you. I can't speak Swahili, and neither can you. You can't swim the Atlantic Ocean alone, and neither can I, nor can anyone else. You can pick up a soda can, and so can I, I speak English, and so do you.
<Negative statement>, neither <similar negative statement>.
<Positive statement>, or <similar positive statement>
Or and nor work similarly.
I can neither sleep nor stay awake to read. We can either go to Seattle or to Los Angeles. We can't go to North Korea nor to Iran. We can go neither to North Korea nor to Iran.
Then there's "but", which invokes an exception, <negative> but <positive>, or <positive> but <negative>
I can swim, but I can't fly. I can't fly, but I can swim. I can't sing, but I can recite poetry. You can read and write English, but not Swahili.