Was the dreadnought kept a secret by the Royal Navy or did they display it for the world to see? When did the Germans find out such a ship was being built or was built? How did the Germans find out?
The drive for the all big gun battleship was well underway by 1904, before Dreadnought; the US "responses" (S Carolina class) were laid down before it, and the Japanese model (per Breyer, 1973, p. 331) was only completed with two calibers because of a shortage of heavy guns. So the idea was no secret. Even before its fitting out, it appeared in Jane's (for 1906, p. 42) with some speculative figures withheld by Admiralty request, but much correct like rough displacement, HG and arrangement, and shipyard, with a photo of the launched hull. The speed of its full completion was arguably a shock (one year, plus final fitting out), but the fact of its existence and its basic characteristics were really not once the uncommissioned hull was in the water, despite the public and nationalist responses to this remarkable evolution. (Jane's for 1906 notes this on page 9 as upsetting the old order.) True, no details were released, so that was a secret, but everyone was aware of the trend. (Note Breyer 1973 p. 50, n70) Massie points out that the construction of Nassau, the German response, was halted while Germany tried to ascertain in 1907 the full capabilities of Dreadnought, which they'd seen demonstrated at that point. (Massie 1991, p. 486)
That doesn't mean the Germans didn't seek out more data, or get things wrong. For example, they famously screwed up their response to the advent of Fisher's first battlecruiser, Invincible, and built the sadly under-gunned Blücher that, like everything associated with that poor man, got the short end of the stick in battle early in the war. (Its WW2 namesake also saw an ignoble end during the invasion of Norway.)
Breyer, S. 1973. Battleships and Battle Cruisers 1905-1970. NY: Doubleday.
Jane, F., ed. 1906. Fighting Ships. London: Sampson, Low, & Marston.
Massie, R. 1991. Dreadnought:. Britain, Germany, and the coming of the Great War. NY: Random House.
The central point is that people got wind of it early and the trend was already underway, so not a total shock. The US and German models took far longer to build, which was itself a matter of concern in an arms race. But they knew of the vague details in 1905. Seeing it in operation, of course, was another matter.
[edit: a bit of Massie, forgot my copy was here / edit2: 'welk' isn't a word in English]