I bought a pretty weekly planner at Barnes & Noble, and found a pen with purple ink to write in it. What can I say, I like pretty things!
I started out just by writing down everything I ate as I went along each day, not even worrying about counting calories. Knowing I was going to write it down helped motivate me to make good decisions at each meal, including considerations of the nutrition and the portion sizes. I made sure I stayed honest and didn't give myself the option to skip over meals or leave things out. Writing it down was going to be pointless if I didn't include everything! I also enjoyed glancing back through the pages and taking a certain amount of pride in what I was accomplishing.
I eventually started using the same book to record my exercise, weekly weight record, vitamins/medication, and any information that felt important in my journey to better health. When a year passed, I'd lost over 50 pounds! And just before I finished out the book, I became pregnant! I chose to complete the book regardless simply to ensure that I'm making my health a priority, even though I can't concentrate on losing weight right now. Once it was filled I went out and bought another pretty book and plan on filling it too, and I plan on continuing writing in the planners indefinitely.
So I'd say do whatever feels comfortable for you, but make sure to find something that you can stick with in order for it to help, whether it's a journal, an app on your phone, a spreadsheet, whatever.
Good luck!