I just had to put down my cat of something like 13 years. I loved him, he gave great snuggles and was quite the troublemaker when he wanted to be.
I knew something was wrong with him, I thought it was his diet or something, but then he got really, really skinny, and I thought, it is because I changed the food. He just doesn't like it. And then I came home one day and he was walking down the steps to greet me, as he always did and he stumbled. And then I knew. I just knew. I took him to the vets the next day and paid all kinds of money to find out what was wrong. He had kitty cancer and there was no saving him. He had to be put down. It was friggin crushing. I still get teary about it now.
There really isn't going to be any making her feel better at first. The best advice I can give you is to not down play it. No talk of it "just" being a cat. Just let her be sad. That is totally normal and what is needed. And when she needs it you can be there to make her feel better. Maybe get her something to remember him by, so she knows you understand it is a big deal for her.
Just think of how you would want someone to treat you if you lost something you loved, and do that.