I LOVE my Diva Cup! I was totally grossed out by the idea of it when I first heard about it, but after having my 2nd baby, tampons just weren't working as well anymore.
As others have said, there is a learning curve to it, so don't give up. I think it took me 2 or 3 cycles before I really figured it out. And in the 2 1/2 years I've been using it, I've only had once cycle where I just couldn't figure it out for some reason. I sometimes use a pantiliner right when I insert it just in case it's not quite right and I have some leaking, but that is rare.
It is actually not nearly as messy as changing a tampon, once you get the technique down. Since the cup forms a seal, all the blood stays inside the cup, so your fingers should not get bloody. When removing it, you want to make sure you are positioned over the toilet so if any blood spills out, you don't make a mess on the floor or your clothes.
What I like about it is that if I know my period is coming, I can insert it that morning, and then I don't have to worry about it until evening. That's especially nice if my period is due when I will be at work. I've never had to change it in a public place.
It is FABULOUS to have on vacation, especially on the travel days.
I will NEVER go back to tampons again.