A training journal is never as important as when you're trying to lose body fat. Your training journal is going to provide some of your most valuable feedback on how well your diet is working for you. You're not likely to get a lot stronger while dieting down unless you're relatively new to lifting weights, but if your training journal shows that your lifts are going down, it's a pretty good indication that you're restricting calories too severely and possibly burning muscle as well as fat.
Again, you can keep your training journal in a variety of formats. The most important information to record is the time of day, the exercises you do, the poundages you use for those exercises, the number of sets and reps you complete, and how it feels. This information will provide you with valuable feedback not just about your diet but about how your body responds to exercise. It's also the beginning of a continuous log that will show you how much progress you've made since you started working out and let you see at a glance what your most effective workout programs have been.
How can you discover if the program you are doing is working if you do not have a road map for getting there. Pick a goal...document your progress...see if it's working. If not...CHANGE YOUR PLAN!