Every major institute hires trainee faculties through

• Direct recruitment
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• References

Mostly for both engineering and medical coaching, IITians and NITians are preferred choices though for biology subjects MBBS, BDS, Ayurveda/ Homeopathy, MSc qualifications are given preference. You can also join them easily if you can get some previous teaching experience from elsewhere.

All coaching institutions provide quite an elaborate training to teach them teaching skills, interaction with students, doubt classes, fun coaching styles, test paper preparation etc. It usually takes 6–12 months before a faculty gets a chance to teach 11th and above batches.

Hope it helps.

All the best!