Should I not eat and not exercise or should I eat and exercise?
Go here BMR Calculator and plug in your stats and see what your BMR is for calories. That will help you in deciding how many calories your body naturally burns on a daily basis. Like if you did nothing but sleep, your body would burn this amount of calories.
Once you have that number you could eat below that number and lose weight. Exercising when it comes to weight lose just helps with adding to the caloric deficit, since you need to eat less than you burn in calories to lose weight.
Diet is key though and a big factor, because when it comes down to it, you can't out exercise a doughnut. Doesn't mean you can't have doughnuts and lose weight, just means you have to know how much your taking in, in order to know how much you have to burn or vice versa.
Here's a good link that lists exercise & calories burned per hour:
Hope that helps you out!