British decryption methods operated out of the army and navy. The organization on the British Navy side was called Room 40. It was a very secret organization that was meant to intercept German messages. It was the organization that intercepted and encrypted the Zimmerman note. In WWI the Directorate of Military intelligence was set up. Section 1 contained "C&C" which was responsible for code breaking. In 1919 the MI1 and Room 40 merged to form the Government Code and Cipher school.
A well known Russian cryptographer was Ernst Fetterlein. He became the chief cryptographer for the Tsar of Russia and held a rank of General-Admiral. He and other Russians solved German, Austrian, and British codes. However when the Russian Revolution came he fled to England and got accepted to join Room 40
The French had 8 stations for intercepting messages: Maubeuge, Verdun, Toul, Epinal, Belfort, Lille, Rheims, and Besancon, and during the war they set up even more, even one in the Eiffel tower. With all of these stations they were the most prepared for decrypting in the war. Over the course of the war the french intercepted over 100,000,000 words from the Germans.
The US started employing native american tribes to make codes such as the Cherokee and Choctaw tribes. The US also had many decoding sections too. One was the Military Intelligence Section 8 which was led by Herbert Yardley. Another was the Riverbank Laboratory in Chicago. This was where Elizabeth Friedman, William F. Friedman, and Agnes Meyer Driscroll worked.
German and Austrian coding proved to be successful as it led to victories such as the Battle of Tanneberg. The Germans required that a communications on the front lines were to be in "three-number code". When it came to communicating between divisions, corps, and army headquarters they used the ADFGVX cipher. The ADFGX and ADFGVX ciphers had connections to morse code and when they were broken they caused a big change. After Georges Painvin broke it it m led to the decoding of the Zimmerman note. It also allowed the French to intercept and decode a message that let them know when the attack would come, the message would later be known as "The Radiogram of Victory".
http://encyclopedia.1914-1918-online.net/article/room_40
https://en.wikipedia.org/wiki/MI1
https://en.wikipedia.org/wiki/World_War_I_cryptography
https://en.wikipedia.org/wiki/Ernst_Fetterlein