It's one of those things that sounds like annoying jargon until you can do it. For me it has also involved literally sitting down and just acknowledging to myself whatever it is that I am feeling. I have to draw on all those things I rolled my eyes at so hard and so long when I started therapy.

"How is my body feeling?"

"Where in my body am I feeling [whatever intense feeling]?"

"Am I breathing? How 'bout I breathe a coupla times and see how that feels?"

"How 'bout dropping my shoulders and unclenching my jaw and stuff?"

Just be there. With your feeling. Noticing that the feeling is there, noticing what that's like in your body, noticing whether it changes your breathing or your hearbeat and then deliberately loosening your body and taking full, slow breaths.

Look at that. You're still alive. The unpleasant feeling is happening and you've been with it for a few minutes now. It's a feeling. It is telling you something. Don't shoot the messenger, invite her in for tea.

I have found it enormously helpful to keep checking in with my T about my progress with this skill. She'll often ask what happened to me or what I did during or immediately following a difficult time. It's not a test ("mwahahaha you went and ate donuts instead being mindful? you fail!") just a long process of noticing what I can do to be gentler with myself and stay present for my feelings. That way, I'm less often stuck in a fog of vague unhappiness and anxiety of feelings left unattended.