LR MUA wrote:
Blowdrying it straight with a big round brush then going over it with straighteners will smooth out any hair. Work in small sections and make sure you've got a bit of tension when blowing/straightening each piece - you don't want to pull so hard as to stretch the hair but just a bit of tension to pull it straight and straighten the roots.
I'll second this. I have naturally very curly hair, but it's not super thick so I can get away with just using a flat iron over it. Blowing it out straight, then going over it with a flat iron seems to get the best results (even for me) but if it's even a little humid or my hair gets wet somehow it will go back to being curly. If you're really wanting to keep it straight and not deal with the upkeep, I'd go for one of those keratin straightening treatments at a salon. It will stay straight no matter one and the upkeep seems to be only as fast as your roots come in.