Check out . They were asia's first low cost airline and are part owned by Tony Ryan (of Ryanair fame). As far as I know they fly from singapore to bangkok, Hanoi and Ho Chi Minh City, so you would proably have to go via Sinagpore; but as far as I have heard it would be significantly cheaper than flying with a national carrier.
For example the 10:40 flight from Bangkok to Singapore on 11 Oct 05 is the equivilant of €43.97 (including taxes!) and the 15:50 flight from Singapore to Hanoi is €57.29. Total cost is €101.26.