I dont really struggle with this so this may or not be helpful to you, but this is what I do and maybe its why.
Every exam I follow a very specific routine.
1)lay out the pens you need and keep one or two backup pens
2) ground yourself like the post above said. If your mind is racing coz you came late or you're stressed just breathe and settle yourself down. Remember that at that point in time there is nothing you can change about whats in your head. The only thing you can change is whether you stress or don't, and clearly stressing ain't gonna help
3) while they're getting the exam set up, work out the times in your head if you can (for when you should finish each question) and when you're allowed to write just jot it down somewhere on the page and try and stick to it. Also calculate roughly how much time you will have left over if you follow the schedule correctly (this allows you to use extra time when needed).
4)i repeat a mantra to myself everytime something along the lines of "you got this, read each question properly and have and keep an open mind" (if you've gone through the whole syllabus then the answer is somewhere in your head, you just need to relax sometimes for it to come out) . My school is catholic so we also say a prayer.
5) the first 10 to 30 secs i skim through the entire paper extremely quickly, just looking at one or two words of each question to have an idea of what they gonna ask me about. Also you get an idea of how many questions there are so you know you should be at the halfway point before half the time is up ideally. If its an exam like English you should work out the times we'll before the exam coz the structure is always the same.
6) at this point start working my way through the questions. I highlight the key words in the question then start answering. You should spend roughly a mark a min at most. If you spend to long on a question just leave it and come back. I put 3 ticks at the top of the page if I think i answered evertyhing correctly, I put two ticks if I answered and I'm somewhat unsure, I put one tick if I answered but almost guessed. I put X's at the top if I missed questions on the page. This way I can easily flick back if I have extra time and try a get each page to 3 ticks.
If you're not finishing the paper in time then maybe there is a problem with revision. Make sure you've done questions and have gone through the syllabus twice. Also, when it comes closer to exam season you should be timing yourself when you do questions.
Lastly, if you're stressed it won't always mean you will do bad. My friend always was nervous and his legs would shake like crazy in the exam hall, but he always got decent grades and now does eng at cambridge.