I'm an ex-paramedic.
This is what I always told my patients:
Hyperventilation is NOT solved by breathing in MORE oxygen (even though it feels like it!)
If you've got to the shaky panicky stage (with pins and needles/numbness in hands/feet/lips etc) then you've actually been breathing in TOO much oxygen.
This is usually caused by one of two things:
(a) A patient has just suffered a nasty emotional shock and gulped in several huge breaths in succession. This is the most obvious and understandable reason.
(b) However - many, many people live large parts of their lives in a kind of CHRONIC, MILD panic:
EACH intake of breath appears normal, but is actually deeper/slightly more often than their body needs. The extra carbon dioxide builds up over time.
Think of this as a kind of bad habit - like biting your nails or picking your nose ...
SO, your body has used all this lovely oxygen, and in turn produced lots of carbon dioxide.
This carbon dioxide is now charging round in your bloodstream, causing all these weird feelings all over your body.
To get back to normal, all you need to do is get rid of the extra carbon dioxide.
Simples. 
The best way of stopping a panic attack? (taken from my 11 years of 999 experience) ...
Understand how your body has got into this mess ...
That even though I had turned up in a flashy ambulance full of expensive equipment, I didn't need to use any of it ...
All you had to do was breathe out more than you breathe in...
I used to get my patients walking about slowly (which helps to calm the shakes) ...
Doing something boring (tidy a drawer, wash up, do some weeding, ironing, whatever) ...
And put some music on.
Then - and this is the magic bit - get them to hum along to the songs.
Keep doing the mindless tasks, and hum.
The humming will naturally slow their 'in' breaths ...
And help to prolong their 'out' breaths.
And that is LITERALLY all they need to do.
They calmly breathed out their extra carbon dioxide and returned to normal.
But, most importantly, they understood WHY it happened in the first place ...
That all those frightening feelings were not signs of an impending stroke or whatever ...
It was just that their body had got out of balance.
And, once they followed instructions and realised they had cured THEMSELVES ...
They no longer had the awful fear of it happening again.
X