Well, if you're tracking the calories you could technically eat whatever portion sizes you want, as long as the total stayed within your limit. Or are you asking how to figure out how many calories are in a certain weight of food? If it's a packaged food, the label will give you the nutrition information for a named weight of the food. If it's not packaged, like a cup of uncooked zucchini, for instance, you can use an online calculator like Calorie King that lets you put in foods by cup or ounce or whatever:
http://www.calorieking.com/
You can keep the totals by hand, online, or use an app for your smartphone. I use a calorie tracking app on my iTouch called LoseIt that does it; but there are also lots of online ones that people here use.
If you want to have standard portion sizes to aim for, to "re-educate" yourself on proper portion sizes (I had to do that) one way is to look at an exchange system, which is based on a certain number of servings of meats, fruits, starches and so on to eat per day. Here's an example at the Mayo Clinic web site, for
fruits (here's the link to the
main page on exchanges, with links to different foods at the bottom).
Here is also a nice slide show from the Mayo Clinic that shows portions visually:
Portions vs servings
ETA: the exchange plans above mention "diabetic" exchanges but it's the same method you use to construct a healthy diet for non-diabetics. In fact, I pretty much used this system to organize my calorie-counting diet.
portion size
. The beauty of calorie counting is that you CAN have a little extra as long as it fits into your plan. There are really no set limitations other than your daily total of calories. Learning the recommended portion size can be helpful for higher calorie foods like rice and pasta, but honestly the recommended size is just a guideline that is not right for everyone. For example, my box of pasta says a portion is 320 calories. I choose to eat less pasta than that, and add more vegetables to my sauce. A serving of salad or veggies is about a cup. I triple this amount to add filling power to my meals. I also like to have a double serving of protein, and half a serving of carbs. Once you learn about portions, there is plenty of room to tweak the recommendations to fit your plan. Let your food log be your guide. If you see that your weighed serving of rice will cost you too many calories for the day, cut it in half next time. Divided plates can be helpful to determine portions as well. Wal-mart sells nice divided Corelle plates that don't look embarrassing to use. Over time it will become much easier 
