Portion size, portion size, portion size.
Like dress sizes, portion sizes have also gotten bigger over the years. No big mystery there. But I think for people new to healthy eating (I don't want to say "dieting" here) portion size is one of the trickier aspects. Figuring out the math of your weight (BMI, BMR, etc) is a bit more straight forward than the general advice regarding how much of what any one person needs. We've gone from hunting and gathering to carefully constructing (or not so much) our dietary intake.
Our eyes and our stomachs are little help here. So our minds have to do the work. I think meal planning plays a huge part in this. The other part that I think is very important is our serving dishes and storage containers. As many nutritionists point out, one of the easiest changes you can make is to use smaller plates and bowls. If you use a large plate do you feel inclined to fill it to the lip? Or do you know how much you need?
Another tip I really love is putting leftovers away in separate containers that are pre-portioned. I love Ziploc's Twist & Lock in the 2 cup container (as well as the similar Target version). Unlike some other containers, the 2-cup container has a line on the side where 1 cup and where 2 cups are. It makes measuring things out much easier when I don't have to take out the measuring cups. By putting them in smaller containers, I feel more comfortable grabbing & going in the morning when I know I haven't filled a very large container to the brim, no matter how healthy the contents.
And for all of the stuff I shouldn't be having? I use Rubbermaid's 1/2 cup containers for most things (other than butter, lard, oil, etc.) if it fits, I don't fret. Half a cup of hummus with carrots, half a cup of guacamole. Neither are worth fretting over (but still remember to count the calories).