Menstrual Cups

Amb
Hey ladies!
I had no intention of ever using a menstrual cup because they weirded me out, but after hearing so many people talk about how great they are, I broke down and bought one. I started using it today and I like it, but I have a few questions.
1. Any tips for getting it out? I’ve found that I’m a little clumsy with it and it’s a little challenging to not make a mess. 
2. How do you clean it when you’re somewhere in public like at work? Do you use a certain product?
3. After cleaning, how do you dry it? I figure paper towels are maybe not a good idea because the fibers could stick to it? 
I know these are probably weird questions, but I want to get the best use out of it possible. I’m hoping to never have to buy pads or tampons again. They’re expensive and they are ruining the planet!