Proficiency in English is something very much required in aviation. One other major accident I remember is the Charkhi Dadri mid-air collision, which resulted in 349 fatalities, and one of the major reasons was believed to be the poor English of Kazakh Airlines crew.
Keeping such importance of English in mind, and the need to standardize English testing and training, the ICAO has issued Guidelines for Aviation English Training Programmes.
Training
Candidates are trained for Aviation English in a very similar way to it would be for any other purpose, other than ensuring the following points:
Use of operationally relevant, work-related language.
Exposure to an aviation environment.
Practical training activities such as Listening practice in ATC lab.
Testing
The Test of English For Aviation is a test Developed by Mayflower College in accordance with ICAO's ratings.
Here is how the candidates are tested in TEA:
TEA candidates can score from Level 1 to Level 6 but most candidates score Level 3, 4 or 5. Candidates are awarded a mark from 1 to 6 for each of the 6 skills: pronunciation, structure, vocabulary, fluency, interactions, comprehension.

Read this document