Hi there! I'm wondering if anyone had any advice on how to make the cake board stand up at the back like in this picture? Thank you! 

What are you making the board from?  Cardboard, foamboard, gumpaste?  I'd insert a couple bamboo skewers in the bottom of the...that should work fine.

Like Jeff said, use styro or foamboard, cut off a slice so yu have a flat section and stick some toothpicks or skewers in which will then stick into the cake holding it up.