How does someone join the Civil Support Team as a CBRN Specialist in the National Guard?

Something you should research is are there NG units in your state that support disaster preparedness and relief. They might have slots for CBRN soldiers.

Those are as far as I know AGR (Title 32 Active Duty) positions. As with any AGR position it's an application process. First there is a vacancy announcement, it will set out the area of consideration (grade, MOS, duty status, etc), and the eligibility requirements (OPAT, PULHES, security clearance, ASVAB, special qualifications, etc). The announcement will also let you know what you need to build your packet, generally at a minimum a traditional M-Day applicant will need to submit an NGB 34-1, RPAM, and a copy of their ERB (work with your FLL and Admin NCO). Once packets are submitted there is a board (interview) and the selection is made from there.