"I eat the salad with oil."
Translation:Je mange la salade avec de l'huile.
French nouns rarely appear without the article in some form—here, the partitive article. I think it's because French has to use the partitive here—de l'huile gives the meaning of "[some] oil." Without the de it would be just "the oil," which doesn't convey the meaning of the sentence.
Because the sentence says "I eat THE salad", which means it's a specific salad so you use "la" for "the". But for the oil it's just oil, not THE oil, so you say "de la" (or de l' in this case and du if the word was masculine.) Basically, you should think of du or de la as meaning "some". You wouldn't say "I eat some the salad". If it said "I eat salad with oil" then you would use "de la".
It's just that you need a definite article with most of the nouns:
de - represents that I eat SOME oil;
De l'huile > De la huile > The h is mute and the next letter after it is a vowel, so la becomes l'.
Je mange du riz. > du - de le;
Je bois de la bière. > here, the noun (bière) doesn't begin with a vowel or a mute h, nor is it masculine, so it will be just "de la".
Also, if a noun begins with a vowel OR a mute h, it will always be de l'. For instance:
Je veux de l'ail. > le contracts to l';
Je mange de l'aubergine. > la contracts to l'.
Nouns in French appear with an article, be that indefinite (a/an), definite (the), or partitive (some). For noncountable/continuous/mass nouns such as "oil," an article still must appear. The partitive article de l' applies here because it means "with [some] oil," as opposed to just "with the oil." Even though in English we often drop the "some," it's required in French. So we can't say "avec huile" because French doesn't allow dropping the article.