Make a furnace using 8 stone. Then place wood in the top slot (NOT wood planks). Then use any wood or coal to make charcoal. Once you have a piece of charcoal then smelt another wood (not planks) using that charcoal and boom achievement.
Update May2019: It seems a lot of people are having issues with this achievement now. For some of you make sure you are actually playing the correct version of Minecraft associated with this achievement since there are multiple Minecrafts on Xbox One. Also thanks to xPut Name Herex who discovered the furnace needs to be brand new, meaning the first thing made with it must be smelting wood with charcoal. So you will need a separate furnace to make the first piece of charcoal.