One of the best ways I have found, to resist the temptation of eating unhealthy foods, is to not buy them at the grocery store.
Just like Eliminate Cancer said, after committing to a life without greasy foods, eventually you will not crave this type of diet. I actually feel sick when I do eat something off my healthy diet. High sugars and sweets make my heart race and grease just sits in my stomach like sludge.
So if you are not surrounding yourself with unhealthy foods, by not buying them at the grocery store, you have to come up with ways to avoid buying junk at the store.
First, eat something before going shopping. Yes, the old myth about buying out the store when you are hungry IS TRUE.
Go shopping once a week. By shopping once a week, you can plan out your meals in advance. This alleviates going to the store every night when you are already hungry and trying to decide what the quickest fix will be.
Finally, drink lots of water throughout the day. By drinking water, it makes you feel full. Maybe chugging some H2O before you hit the store will be just what the doctor ordered. Good luck ;-)