There are many ways to overcome sugar addiction. However, they can be broken into two categories: Physical and Mental. (Or maybe Logistical and Emotional.)
1. Physical/Logistical - These are easier changes to make.
Remove hidden sugars from your diet.
Check sauces, breads, all breakfast items, all snacks, pretty much all prepared foods. Compare ingredients across multiple options, and choose the one with the least sugar, but MORE IMPORTANTLY, a short ingredient list. If you simple check the grams of sugar you will almost for sure be buying something with worse ingredients.
Look for ways to replace, reduce, or remove things that are intentionally sweet.
Do you put sugar in your coffee? Cut it in half, then cut it in half, then cut it in half, until it is not very sweet, or, if you still like the taste, not sweet at all.
Do you like something sweet after dinner? Find out if you can have some slices of fruit instead of ice cream. Or, like the coffee, start with a plate that is half fruit and half ice cream, then reduce the ice cream further, then substitute sweetened yogurt, then move to unsweetened yogurt.
2. Mental/Emotional - These are all the things that make it seem impossible to do the changes I've described above.
These are the days you feel so stressed out and overwhelmed you pull out the whole tub of ice cream and eat it straight from the carton.
These are the moments when you sit in front of the TV after a long day and suddenly the entire box of Chinese take out has disappeared.
These are the afternoons when you just can't make it without a giant latte or chocolate bar; this is what gets you through the day.
This is the part of the equation when you tell yourself you're going to change... and you don't.
This is the struggle of deciding to stop, and then you can only think about the thing you are stopping. And when you finally "give in" you eat three times as much.
Some people can just decide to do the physical changes and they are done. For other of us, including me, the mental changes MUST be addressed to lay the foundation for the physical changes to succeed.
The mental changes are addressing the problem behind the sugar. The problem behind the sugar may or may not be known to you. The problem behind the sugar may or may not be clear when you think about it. You can begin by looking backward over the past week and thinking about what PRECEDED the sugar binge or failure to stick to your resolution.
Bad day? Fight with the spouse? Kids going crazy?
Horrible boss? Lonely? Bored? Angry? Tired? Annoyed?
If you don't know, or you do know, but still can't seem to make headway, then you should seek support - read, ask a friend, find a professional, whatever it is that helps you find a clear path and system to address the problem behind the sugar.