Learning to stop anxiety and panic attacks isn't difficult, but they can be very difficult to conquer on their own, without any guidance. Here is how I learned to stop these attacks forever.
When I first had periods of panic, the first symptoms I noticed was that my chest felt heavy, and it was difficult to breathe, almost like there wasn't enough oxygen in the air. I found out a few weeks later that the perception of breathing difficulties, along with an elevated and even painful heart rate, are the two biggest side effects of panic attacks.
The first thing that will help you stop panic attacks is realizing that these attacks are nothing more and nothing less than your body reacting to stress in your life, which activates the biological fight-or-flight reaction. There is no physical cause, and these episodes do not harm your body or pose any danger to you.
You might not even realize at first that you're having a panic episode. You might think you're having a heart attack, or your lungs aren't working properly, or you are sick, but all of these feelings are physical manifestations of problems that are actually entirely internal. Tell yourself that you are fine, these attacks don't kill anyone, and that this attack will pass, will help you get through your next episode.
The next step is to find their cause. Did you have panic episodes like this a year ago? What about six months ago? What changed? If you can't think of any significant, stressful differences in your life, think back a month at a time until you create a shortlist of possibilities. It's even possible that many little problems contributed to one MASSIVE problem.
Your panic attacks might not be even caused by extremely recent concerns - they might be resulting from an elevation of problems or anxiety that had been building up over months or years and finally reached "critical mass", or they might be symptoms of a slowly-growing mental affliction, like generalized anxiety disorder or depression, that your body was not able to sustain anymore without going "overboard."
The final step is determining whether or not you can cure your own panic attacks. The key for self-treatment is being convinced that what you're experiencing, are, indeed, panic attacks, and not something seriously wrong with your body. I personally required a couple of doctor's examinations before I believed that. That second visit marked the day of the last severe attack I've ever had.