The first way is going cold-turkey. That is, you literally change your diet entirely overnight, cutting out all the bad stuff and replacing it with the full "good" diet. This is what following the SCD and GAPS Diet requires for full healing. People do it, but generally with a lot of support or help from parents. For those of us with weight issues, this may be a slightly more risky choice. From personal experience, I have found that if you are going to go this route, there must be ample planning and experimentation beforehand. Before you switch over to your ideal diet, you need to already know how to cook what you're going to eat, which recipes you really like, where you're going to buy your food, how much it costs, how much you need to eat a day in order to get enough calories, etc. In other words, you should have tried pieces of it out in real life and prepared for your new diet before you actually start it. The risk of not being completely prepared is not eating enough, losing weight, getting sick, or getting overwhelmed, hungry, and burnt out so that you quit and go back to eating the bad stuff. Also, in the cold-turkey version, you're going to have to throw out or give away a lot of food. There are some things in your pantry and fridge that you should not eat and should not be tempted to eat, so you've got to chuck it. In the cold-turkey version, you've got to do this overnight, and that can spell food waste if you don't find someone to give it to. I am loathe to encourage food waste. But in terms of healing ability, there's no question that this approach is best, because you are breaking the cycle of eating that feeds the bacterial overgrowth in your gut, causing leaky gut, indigestion, reflux, constipation, and other G.I. symptoms. By doing it this way, you should be able to feel symptomatic improvements pretty immediately.
The second approach is gradual, eliminating foods step-by-step in a systematic approach. This was the way I did it, over several years. I did it this way mostly because I didn't know what the "ideal" diet was, I just knew that I had to get off sugar, wheat, and dairy. From there I learned more about what I should and should not eat, and made further changes. Although it does not have the immediate therapeutic benefit that an overnight change does, this approach is likely to be more sustainable over the long term and a little less risky. You will be able to take the bad stuff out, step-by-step, getting used to a little change and congratulating yourself for it, then moving on to further improvements. I have found that this approach builds a sense of accomplishment and pride that you are truly healing yourself, slowly but surely. Bit by bit we get used to "living without" those things we used to like to eat, and finding yummy things to replace them with. It is less likely that you will get overwhelmed by cravings if you haven't eliminated all the things you have cravings for (e.g. donuts, chocolate, potato chips) all at once, but one by one. This can be done over whatever length of time works for you; from a few weeks to a few years (the shorter the better, obviously). But keep your eyes on the goal: a 100% clean, whole foods, all-natural diet following the GAPS (or SCD) guidelines.
If you're going to take the gradual approach like I did, I have a few suggestions. Use the table I created to prioritize the categories of foods and food-like substances that you need to eliminate and replace. The first things to eliminate are obviously junk food and toxic substances like soda, candy, fast food, artificial ingredients of any kind, etc. This includes the food-like substances/junk food labeled as nutritional supplements that your CF docs tell you to eat (i.e. ScandiShakes, Carnation shakes, pre-packaged G.I. tube formula, etc.). The second thing to eliminate is sugar (all concentrated sweeteners including white sugar, brown sugar, molasses, maple syrup, agave syrup, brown rice syrup, corn syrup, high-fructose corn syrup, fruit juice concentrates, etc.). This is a hard one because most Americans are addicted to sugar, even when they think they eat "healthy". Sugar is a physically addictive substance and you have to "break" the addiction. I suggest going completely sugar-free until the cravings disappear, then reintroduce safe sugars like honey and sweet fruits in small amounts (we'll never be able to binge on sugary stuff again, so practice moderation even with healthy sugars). If the cravings return, repeat the process. Even after you're on your ideal diet, you may need to do a sugar fast (eliminating the safe sugars) for a few days once in a while to keep things in control or to alleviate symptoms like a yeast infection.
It took me two weeks before I stopped having cravings for sugar. That was one of the hardest things I have ever done, but it felt so good to be addiction-free! I think it would have taken me a shorter amount of time if I had eliminated sweet fruits and honey. It was a serious exercise in will power, but it's just like getting in shape - the more you do it the easier it becomes. The will is like a muscle. Every stage you accomplish makes you stronger and makes it easier to accomplish the next stage. I actually cut out sugar and cow dairy at the same time, but I let myself eat goat cheese. From there I eliminated wheat. Then all gluten. Then all dairy. Then all bad oils/fats. Then all grains. Then I started the SCD/GAPS diet, my "ideal" healing diet. So, as you can see, it's been a long journey. From the point at which I first broke my sugar addiction to the point at which I started the GAPS/SCD, it took about 2.5 years. It may have taken a shorter amount of time if I had known what I should eat (the GAPS diet) rather than only what I should not eat. But you know. So maybe it will be quicker for you. Remember that with every thing you eliminate you must ideally replace it with something healthy so that you don't run out of things to eat. Look over the chart for more info.
You have a lot of options when it comes to moving towards your ideal healing diet, so do what feels right to you. Listen to your body and your intuition, and exercise your will power!