In addition to Ryan's excellent advice, you should know ahead of time how many questions will be on an exam, and how much time you'll have to complete the exam. If you have a tendency to rush through, make note of how much time you should need per question, and after 5 or 10 questions, check your time. If you're way ahead of schedule, take another deep breath and slow down to read more carefully. (I don't suggest this to someone whose nerves distract them and keep them from finishing on time.)
Another option is to answer questions out of order. Skim through and start with the ones you know you can answer easily, then get the ones you're pretty sure you know how to do, but aren't quick answers. Then go back and take your time on the ones that you need to work hard on, knowing you have at least gotten a chunk of easier ones done. When I give paper exams, I tend to order questions by difficulty so there are a few nerve-calming questions on the first page and the difficulty increases. But, computerized and standardized exams often randomize question order, and some faculty never think about the order of questions. So, with those, you could wind up with the hardest question on the first page, which is panic-inducing for someone with even mild exam anxiety. If you know that going in, you won't panic as much if prepared to look for the easy ones first.
People prone toward exam anxiety also should avoid studying at the last minute or pulling all-nighters before an exam. Sleep helps us handle stress better. Keeping up with studying all along is a good habit for everyone, and essential for someone who feels more and more stress as exams get closer.
Try doing your homework as if it were an exam. Review the lecture material before starting the homework, and try to do as much as you can from memory without looking things up. Then, when it's time for the test, just think of it as a long homework set.
Some students get worked up listening to other students before an exam. There's a lot of nervous chatter before exams. I suggest that my students who get nervous about exams should enter the exam room as late as possible and do something somewhat active right before the exam to keep distracted from getting nervous.