It is true that the royalty of the British, German, and Russian royal families were cousins. The French, on the other hand, did not have a royal family at the time as it was a republic. Victor, styled as Napoleon V, was the claimant to the French throne at the time, but was not related to any of the Royal cousins closely.

So to answer your question on how they were related, it's actually quite simple!

Kaiser Wilhelm II (Germany) was first cousin to King George V (Britain), and third cousin to Tsar Nicholas II (Russia). George and Nicholas were both grandchildren of Queen Victoria of the United Kingdom and therefore first cousins, with Wilhelm being the eldest of her grandchildren.

Wilhelm was the son of Frederick III of Prussia and Victoria of the United Kingdom, the Princess Royal and eldest child of Queen Victoria. George was the son of Edward VII, son of Queen Victoria, and Queen Alexandra of Denmark. And finally Nicholas, who was the son of Emperor Alexander III of Russia and Princess Dagmar of Denmark (Alexandra of Denmarks sister, making George and and Nicholas first cousins). The relationship between Wilhelm and Nicholas is as third cousins, both being great-great-grandchildren of Paul I of Russia.

So to summarise; Wilhelm and George were first cousins. George and Nicholas were also first cousins. And Wilhelm and Nicholas were third cousins. Pictures of of Tsar Nicholas and King George show that they are remarkably similar in physical appearance.

I hope this answers your question!