The quickest way to lose weight may not necessarily be the most effective way.
The quickest way would be to jump right in, cold turkey into the perfect diet...and for most, that would make things hard to maintain right off the bat.
I'd say the most effective way is to make gradual changes to your diet, like work on getting your breakfast down to where it's healthy, then move onto lunch and finally dinner.
But, to break it down for you...You should never drop down below 1,200 calories/day as a woman or 1,500 calories as a guy.
In order to more easily stay on these diets, its best to cut out all processed food as it tends to be oratorically dense food which won't help you stay satiated on the diet.
Stick to lots of veggies (cauliflower, broccoli, carrots, celery), lean meats (chicken, fish, lean beef, egg whites) and 1-2 fruits per day.
most importantly, count your calories and track them, and weigh your food so you know whats going into your body, skipping this step will mean the difference between success and failure in the long term.
Learn more on setting this up here.