I should probably note that I am not very good at this, and I am way better at dealing with emotion from a past event than emotion from a present event.
I don't think I mean grounding? I mean more like an outlet for expressing yourself. Expressing anything you want to. Sort of, a place where you can listen to yourself? Um... that's what it feels like. A place you feel safe enough to express yourself too, almost like an extension of yourself in some tableau/format. It doesn't really matter what outlet you choose. And it takes time to develop that degree of comfort with such a thing.
So my outlet is writing about what's going on in my life. It took me years before I could journal like that. At first, I wasn't journaling very often because I wasn't used to it, didn't have anything to say, etc. And I also didn't have a spot where I could be assured that I wouldn't be bothered when I was doing it (whatcha writing? or somebody snooping on what I'd written in a paper journal). So at first, I wrote imagining someone else would read it. After a time, I grew comfortable with it, and I made sure nobody else could read it.
After that, when the emotion started to show up, I mean, sort of, saying, yes, that was scary/whatever emotion. Not saying, what are you talking about? This is Snoopy; Snoopy isn't scary. Well, yes, Snoopy can be scary. Or, my computer died about a year and a half ago, and I am sad about it. Not saying, it's just a computer, and it's been a year and a half, man; get over it already. There are still times I want to go back and look at journal entries from then, and I thought I would be able to, and now I can't, so I'm sad.
I dunno. I am sure there are other ways to do this, but this is my method.