Lets see, there I am, nervous and often shaking in my shoes, but I've learned to go ahead and dive in anyway. It usually works out.
For riding horses I work HARD on getting my seat better, heels down, sinking my weight into the stirrups, and making very, very, very sure that I do not have a death grip on the reins. As long as I do that the horses don't seem to care that I am freaking out over something so long as I do not scream.
Both horses and people seem reassured when someone who is terrified just goes ahead and does whatever it is. If I am still nervous and anxious I just go ahead and tell the person or horse, and then I do not have to worry that they might think I am scared because they already know I am scared and they can deal with it.

However I do not get panic attacks, just the usual nerves and being scared.

If it gets too overwhelming I go to my trusty homeopathic combination remedies. They've got them for depression, fear, anxiety, guilt, heavy grief, nervousness, etc.. It took some experimentation to find out the ones that work best for me, and I carry the two that work the best in my purse, just so I know they are there. I use them maybe once a month to once a week or so if it is realatively bad, to several times a day for a day or two for the really bad episodes.