I took French in high school. I refreshed this high school French in 2011-2012 and yet I can’t remember ever hearing of the need to use a partitive article (or for that matter that there is something called a partitive article or Teilungartikel of Deutsch). However in lesson four of Französisch in 30 Tagen, there it is with the following examples.
• In speaking about a menu:
Ils ont de la salade, des sandwichs, de l’omelette, des croques-monsieur, des croissants…
“They have salad, sandwiches, an omelette, croque-monsieur, croissants…”
• In describing the croque-monsieur:
C’est un sandwich avec des toasts, du jambon et du fromage.
“It is a sandwich with toast, ham and cheese.”
The Grammarist explains it thus:
When referring to a noun whose quantity or amount is not specified, French speakers use the partitive article de, which conveys essentially the same meaning as some or any in English.
For example, rather than saying the equivalent of I bought cheese, French speakers always say, I bought some cheese. Rather than saying, Do you have pets? they always say, Do you have some pets? This rule cannot be ignored. If you ask for the cheese or just cheese without the partitive article, French speakers may think you’re talking about a specific amount of cheese or all the cheese in the world—either of which would cause confusion.
Okay, I’m off to make une omelette avec des pommes de terre, du bacon et de l’oignon (ein Bauernomelett).
French would replace the bacon with some fines herbes!
I added some dill :-D!
I found another good site that also includes an exercise to help you to learn this concept: http://www.frenchtoday.com/blog/french-indefinite-and-partitive-articles and includes a few examples of how you talk about specific quantities of my favorite topic, food:
• Un verre de vin (a glass OF wine, NOT DU, you do not say “a glass some wine”)
• Une bouteille de champagne (a bottle of champagne)
• Une carafe d’eau (a pitcher of water – de becomes d’ + vowel)
• Un litre de jus de pomme (a liter of apple juice)
• Une assiette de charcuterie (a plate of cold cuts)
• Un kilo de pommes de terre (a kilo of potatoes)
• Une botte de carottes (a bunch of carrots)
• Une barquette de fraises (a box of strawberries)
• Une part de tarte (a slice of pie).