Here's a rule of thumb, but there are exceptions. Subject = Nominative Direct Object = Accusative Direct Object with "nie + verb" = genitive Indirect Object = Dative
Instrumental is used with a form of "to be/być" and contains this pattern:
pronoun - to be - noun, OR noun - to be - noun,
Examples: He is a boy = On jest chłopcem. The man is a doctor = Mężczyzna jest lekarzem.
And I agree with Jellei, take notes. Straight up vocabulary I have in a spreadsheet, but verb conjugation, cases, declination of pronouns and adjectives, etc, I write out in a notebook. I use the notebook constantly while going through the lessons.
Does it mean financial support? Or a general support from the background, that you agree with whatever he does? Or is it more like taking care of someone by giving them advice and money and help and whatever they need?
Both the English 'support' and Polish "wspierać" have broader meaning, so don't only mean financial one – for example, a company sponsoring the world champion could said this to his sister/brother, in both languages… Somehow I doubt you would say to, for example, Tiger Woods, that "he should stop playing with the sticks already" and "get a job instead". ;-P