Partitive case is one of the most important and very difficult themes in Finnish language. You will use this case really a lot, if you’re going to speak Finnish, so take your time to learn all the endings, changes and using it.
Grammar from Tampere University: formation of the Partitive case in singular and plural, with different types of words; when to use it, with lots of examples, all translated into English. Partitive verbs with examples. Few exceptions. Finally, the object problem: Partitive VS Accusative.
One more table with Partitive formation both in singular and plural.
About Partitive case from The Finnish Teacher, both formation (singular) and use.
Here you can find a short lecture about Partitive case with many explanations and thoughts about using it.
If you want to check more advanced grammar and explanations, visit this page, where you can find information about Partitive stem and different types of words.
Why is the Partitive case so tricky? Read here different opinions.
One more page with short information on Partitive case, with formation and exceptions.