Its going to be completely different to each person, there are also many types of anxiety (i.e. Generalised/Social/Phobias), there is also panic attacks which are different again, but can be a symptom of anxiety problems. If you believe that you have anxiety then you are best to contact your doctor who will assess you on a personal level. There are also many treatments for anxiety, not just drugs. You will find something suitable that will reduce your anxiety for you.
I have Generalised Anxiety Disorder, most of the time it isn't obvious. But I constantly worry and feel like I have a weight baring down on my chest. Sometimes it gets so bad that I cannot breathe, which is often suggested as a panic attack. It also causes me not to be able to sleep at night and I think about the worse case senarios in most situations. I also cannot stand any kind of surprise.
It is a very complex thing, so that is only a very basic idea of how I feel most of the time.