Hello Ayush.

Well COA (Council of Architecture) is a body that conducts the NATA examination but does not conduct separate counselling. The eligible candidates (candidates who have scored the minimum cutoff marks in the two individual components and also in aggregate) have to apply in the desired institute among the participating institutes separately based on their NATA scores for admission into B.Arch course. Along with this, the candidate will have to meet all the other eligibility criteria specific to the institute. 

I will suggest you to visit https://engineering.careers360.com/articles/nata-counselling to get detailed information regarding NATA counselling and admission process.

Hope that helped.

Hello

to get admission through NATA just go to your desired college website and apply through NATA score for B Arch courses, apply for counselling in that college or university and if your score is good then you can get the course.

More details can be found here: https://engineering.careers360.com/articles/nata-counselling