I use a tiny bit of liquid hand soap (not the anti-bacterial kind) and soap it up really well, wash off the suds and pat dry with a towel (I can't really leave mine laying around to dry off right now).
I've had my packer for about a year but I don't use it a whole lot. I also don't like to use cornstarch or anything because it bothers my skin and feels odd, so I just deal with it being a bit sticky lol.