We are also starting to make a transition from a sippy to a normal cup. We're going VERY slowly.
What helps for us is to put just a tiny bit of fluid in the regular cup, so if they spill, they don't drown (or waste all the milk). I also only give Lilah her own cup when she's sitting down, in her high chair. We use sippies for out and about, but now only use the sippies without the one-way valve, to teach her to modulate the flow of the liquid. I'm also planning on ordering her this cup:
http://www.beyondplay.com/ITEMS/T353.HTMThe lid sits inside the cup, and helps control the flow of liquid while also allowing her to drink from the rim of the cup. I also like that once you no longer need the lid, the cup is still useable, unlike other kinds of sippies. I'll let you know how it goes with this one.