When it comes time to take the finals, you either know the material or you don't. The best thing you can do is to acknowledge that you are scared to high h*ll, by understanding and saying to yourself...(this is important) what it is, physiologically, that's causing you to feel that way. It's obvious, but over the years, I've found that I sometimes become "numb" for a short while to emotions when I really talk about the psychological and physiological reasons behind feeling this way. It's kind of like saying the word "hand" 300 times. Eventually, you don't even recognize the word.
Of course, everybody's different, and this might suck for you. In which case: my bad, bro.
As for prep: create a schedule for the next coming week, and set aside specific times to work on specific classes. The amount of time spent on each class will be dependent on your current grades in that class, your goal grade for that class, where you stand in terms of being up to date with the material, and lastly, the day of your final.
If one final is on Tuesday, and the other is on Friday, it might be wise to put in more time, initially, for the Tuesday final, and use the time afterwards to study for the Friday final.
Maybe you study a few hours every day for each class, and then tailor the time to your schedule once the actual exam week begins. This gives you solid preparation beforehand, and allows you to titrate the final concentrations right up to the time you put pen to paper (because I don't use pencil.)
It's really about being able to recognize what it is that you need to learn, and how much time you have to do so. Once you do this math for every class, you'll have a better idea of how to stagger and allocate your time for each class wisely.
Keep calm and final on. Something something doesn't kill you, something something stronger; yeah. Aye.