As Dave said - put outside pedal down when cornering, don't have the feet level on each side. You need to be able to put some weight onto the outside pedal.
Look up and ahead to where you want to go as that's where you'll end up. Keep moving your line of vision ahead to the point on the road that you want to eventually ride over, that might be 30, 40 or more metres ahead (much longer if going fast). If you look to the side of the road, or at a tree or a rock, that's where you will end up going!!
Also (and I know Dave said riding on the brake hoods was OK, which in general it is) but I consider riding in the drops the safest option, especially as you build up speed and/or the surface is less than perfect. Hands are less likely to slip when in the drops and brake control is best there - both for maximal leverage but also for feather like control.
However, some riders, esp women find it difficult to:
a. ride comfortably in the drops (i.e. the bike doesn't fit properly and quite possibly doesn't handle as well as a result)
b. reach the brake levers easily from the drops, esp if your hands are small (in which case some adjustment might be required so the levers are within reach or a different shape handlebar might help)
Keep at it, decending well is one of the great pleasures of cycling. The suggestion to find a good rider to follow down a hill is good one.