Okay, I am just a little confused about "van". Is it sort of a grammar thing? Ex. if I said "My cat is small" it would be "Mijn kat is klein" but if I said "The small cat is mine" it would be "Het kleine kat is van mij." (sorry if that doesn't make any sense, I am REALLY new to Dutch. And I really don't know het vs de)
VAN MIJ is "of me" which is a common way of expressing ownership of something. Van mij gets tacked onto the end, as well as used in sentences with the 'a such and such of mine' type structure.
MIJN goes before nouns/(and names?). There are other ways of expressing ownership and such I believe but, as I'm very new myself, I'm not the one to explain it.
Here are some links explaining ownership in general and Van much better than I can.
These explain Van mij and a little bit of Mijn on the second one.
The rest of the possessives are in the blue box/table on the left hand side, 3rd or so section down from the top.
HET and DE are hard. Basically it's all memorization, as far as I can tell. I was making a list for each of the words that use them, then learned there are far more De than Het, so now I'm just making a list of Het words as I encounter them as the below link suggests. I'm also trying to memorize the article with the word, but I'm not great at that.. (Ha, I started Dutch because it seemed easier; all the gender stuff in French was giving me a headache... Clearly, I did no research first.)
Here are some links explaining Het and De and how to deal with them:
Hope that helps! Maybe someone far more experienced can chime in, add things, correct me if I'm wrong, etc.
A great Dutch DL resource made by the Dutch moderators: "Overview of grammar explanations" at:
This page has many sub-page links among which show: 1. For possessive pronouns you can see the paragraph linked and titled "The possessive pronouns in Dutch". 2. For het vs de, see the paragraph linked and titled on the same overview, "De/Het/Een".