How do local police forces and FBI offices find material and instructors for training? 

According to the FBI website, there are specific requirements for different positions. But, there is nothing specific on exactly how they pick and choose trainers or materials regarding counterterrorism. 

This is what they provide on their website: 

To become an FBI Special Agent

• You must be a U.S. citizen or a citizen of the Northern Mariana Islands. 
• You must be at least 23 years of age, but younger than 37 upon your appointment as a Special Agent.
• Age waivers may be granted to preference eligible veterans who have surpassed their 37th birthday. 
• You must possess a four-year degree from a college or university accredited by one of the regional or national institutional associations recognized by the United States Secretary of Education. 
• You must have at least three years of professional work experience. 
• You must also possess a valid driver's license and be completely available for assignment anywhere in the FBI's jurisdiction.

To qualify under the Computer Science/Information Technology Entry Program: 

• You must have a computer or information technology related degree, a degree in Electrical Engineering, a Cisco Certified Network Professional (CCNP) certification, or a Cisco Certified Internetworking Expert (CCIE) certification. 
• Applicants that qualify by virtue of a CCNP or a CCIE certification must also have a BS or BA degree in any discipline.

To qualify under the Language Program: 

• You must have a BS or BA degree in any discipline and be proficient in a language that meets the needs of the FBI. 
• Current qualifying languages include Arabic, Chinese (all dialects), Farsi, Hebrew, Hindi, Japanese, Korean, Pashtu, Punjabi, Russian, Spanish, Urdu and Vietnamese. 
• Candidates must pass both the listening and reading portions of the Defense Language Proficiency Test (DLPT) and demonstrate a proficiency of three or higher on the Speaking Proficiency Test (SPT) in a critical foreign language.

To qualify under the Law Entry Program:

• Candidates must have a JD degree from an accredited law school.

To qualify under the Diversified Program: 

• You must have a BS or BA degree in any discipline, plus three years of full-time work experience, or an advanced degree accompanied by two years of full-time work experience.

To qualify under the Accounting Entry Program, candidates must:

• Have been certified as a CPA; or
• Possess, at minimum, a four-year degree with a major in Accounting and three years of progressively responsible accounting work in a professional accounting firm or comparable public setting, such as state comptroller or the General Accounting Office.

Other than that, there is nothing I could find that provides any information on the process of choosing materials and instructors for training, except that the counter terrorism training division has a lot of autonomy, and it is essentially in charge of putting together its own training module and then is supposed to find a way to fit that training into the broader curriculum for agents. 

I think this would be a good question to ask the United States Department of Justice in a FOIA request. If we know how the process is done, it will help in creating ways to make sure the trainers and materials chosen to train FBI agents regarding terrorists are not anti-Muslim and anti-Islam. It will help in implementing methods in which unbiased trainers and materials are chosen. This could be a great step in combating against the common misconception of all muslims being terrorists and Islam being a violent religion.