In a word: very. You simply can't outwork a poor diet.
No matter how hard you train, if you are trying to lose weight you can't outrun a greasy burger and a soda.
Let's put it into perspective.
At rest, we burn about 65-86 calories per hour. That isn't a lot, considering a large serving of fast-food french fries can contain over 450 calories. If you were to try and "burn off the fries" by cycling at a moderate intensity, it could take you up to an hour and a half.
This makes exercise a pretty inefficient way to try and create a "calorie deficit", which is often cited as the only way to lose weight (in other words, make the "calories out" greater than the "calories in".
To lose weight, or I should say lose fat mass, you need to change your diet instead. Instead of eating calorie dense foods, such as refined carbohydrates and processed foods, each nutrient-dense foods, such as high-quality meats and vegetables.
(Here is a weight loss "hack" from Tim Ferriss: consume 25-35g of protein first thing in the morning. This will help curve your cravings for carbohydrate-rich foods. This means staying away from your "healthy" smoothie or your juice cleanse.)
For performance, it is equally important to eat properly in order to gain muscle and recover from your workout. Eating for training isn't about matching the calories in to the calories out. Trust me, this is going to happen naturally. Instead, worry about getting as many nutrients as you can. Make sure you are eating plenty of vegetables and get in some protein as soon after your workout as you can.
My diet advice is generally very simple: eat more vegetables, and less of everything else.
If you focus on getting the good stuff in, rather than trying to exclude the bad stuff, you are bound to be much more successful. As Tim Ferriss says "self-control is overrated". Don't rely on willpower and instead set yourself up for success. Plan your meals and cook in bulk. After the first few weeks, things will get considerably easier, and you will notice your cravings for junk food will decrease. Trust me, I have as much of a sweet tooth as the rest of them, but when you are on track it is much easier to stay there.
B.Kin, Canadian Society of Exercise Physiology