Though you can book online directly from airlines company but sometime offline booking or booking through a local travel agent / travel agency could fetch you good discount as they run some promotional offer. I found flightoworld.in which is based in lakhmi nager who is currently offering the cheapest airfare for flight to Bangkok with upto 20% discount. They also promise to provide you with a immediate booking and quick refund. Try flightoworld.in
Don't forget to book a taxi from Delhi airport.
If you want to book cheap flights, it is possible to use one of the sites that were created specially for this purpose. I recommend to look through the collection on https://travelsites.com/cheap-flights/. I use them every time I want to go somewhere as they allow me to save money on tickets.
Cheap flights has its problems. If you want comfy journey you need to pay.