Make sure you get plenty of protein (lean meats, low/no fat dairy, etc), complex carbs (veggies, whole grains, beans, etc) and "good" fats (avocados, olive oil, nuts/seeds); those are what will keep you fullest for the longest amount of time.
I second tigerlilly5909 - you can do it........
About a month. I would say. Some people do better with more frequent, smaller meals but I like bigger meals so I try to skip the snacking or small meals like some people eat. My stomach used to bother me all the time if I didn't have something for it to chew on but after about a month of eating healthy it didn't bother me anymore. I would get hungry but my stomach would not get sick. You'll find that you can go longer without being hungry depending on what you eat. Stay away for lots of carbs especially simple carbs. Load up on fruits, veggies and water to help keep you fuller longer. I still think about food all day but it's not as hard as it used to be to wait till the next meal.
Good luck, you can do it!