So HOW did the Nazis get the Bomb?

I can only assume that their heavy water experiments started as soon as they got into power in 1933, and kept it secret, so that by the time the war started in 1939, they were much more ahead in creating nuclear warheads than what actually happened. They then launched via V2, their first nuke on London, and the UK surrendered.

Then they put all their resources into either launching a second nuke on Washington DC, or sent a massive invasion fleet over the Atlantic to do the same thing?

I've only seen the first episode, but I don't wish to sit through the rest of it, so can someone give me a potted history or is there a website that explains it in detail?