Writing increases your awareness of what and how much you are eating. Furthermore you'll be more conscious of the areas where you can make changes. Many experts say that the simple act of keeping a food diary can also encourage you to eat fewer calories and with that losing weight. People usually notice that they snack a lot more than you realize, don't have enough variety in their diet, etc.
On the other hand writing down your workouts will inspire you to do them regularly and keep you going! You are able to track your progress and stay motivated! After a while, you'll go back in time and see where you've started. Now I can run 10 kilometers (6 miles) but I started with only three kilometers (1.9 mile), I can do more burpees, squats, etc. Sometimes it's funny when you look back and see what was the challenge back then. But of course you have to start somewhere! You can upgrade yourself step by step and beat yesterday results.
Easy. Just buy a lovely notebook and start writing! Or a regular one and make it your own like me ;)
While writing down my workouts has become part of my everyday life, I'm still not consistent when it comes to the food (but I'm working on it). Here are my food/exercise journals. You don't have to have two though. You can write a food journal on one side and workouts from the other.
Give it a try and have fun with it!