First, let's imagine we have two sentences, A and B. The content of the sentences does not matter for this example. "However," means "A is true, but B is also true." simple: I like apples, however bananas are my favorite fruit. difficult: The reading says that popping your knuckles can cause arthritis. However, the professor says that doctors have failed to prove this for decades. "Nevertheless," means A is true but doesn't affect B. simple: He was sick, but he went to work nevertheless. complex: Even though modern science says keeping someone with a concussion awake is not healthy, people nevertheless believe that you cannot let them fall asleep. "Moreover," means that A is true, and B is going to support A. simple: Bananas are delicious. Moreover, they are healthy. difficult: We installed CCTV to deter criminals. Moreover, should someone commit a crime, the CCTV will help the police catch them.

'However' means 'but'. The only difference is that it's more formal, and used more in written language. 'Nevertheless' means 'in spite of this'. It refers back to - and in some way contradicts - something that you have mentioned in the previous sentence. 'Moreover' means 'What is more'. You use this to add more information to reinforce what you have said in the previous sentence. Most usually, these connectors go at the beginnning of the sentence before a comma. If you'd like to try writing some sentences of your own, you could put them in another post or in the Notebook and we can check them for you.