Hey! It's super simple, you'll just have to change one line. New Delhi is on yellow and Airport Express line (Orange).
1. Take the Metro on Yellow line going towards Huda City Centre. 2. Rajiv Chowk will be the next station after New Delhi, get down there 3. Take Blue line going towards Noida City Centre (Not Vaishali) and get down at Akshardham Metro Station. Hope it was helpful!
many of fellow travellers have already told u how to get till Akshardham metro station.. so you can easily go till there.. I would like to suggest you that the temple is at walking distance from metro station so please don't take any rickshaw or cab from station because they will only take a longer round along the flyover just to make money.. go by foot..