Partitive's characteristic ending of -a or -ta denotes partialness, without result, or without specific identity. So it is often used to express unknown identities and irresultative actions. It is also used in contexts where a subgroup is selected from a larger group, or with numbers. It is used in the following circumstances, for example:
after numbers, in singular: kolme taloa → three houses
for uncountables: lasissa on maitoa → there is (some) milk in the glass
for compositions: pala omenaa → a piece of apple, paljon rahaa, a lot of money
for some or any: onko sulla rahaa? → do you have any money?
for negation: talossa ei ole kirjaa → in the house, [there] is no book; mä en lue sitä kirjaa → I will not read that book, mulla ei o tietoa → I don't have any info
with emotions: rakastan tätä taloa→ I love this house
target of an emotion when the agent or the source, cause of the emotion is unknown, such as common sensations to feel tired, to be irritated, to feel amused, to be disgusted, to feel sleepy, etc. → väsyttää, ärsyttää, huvittaa, inhottaa, nukuttaa: mua nukuttaa → I feel sleepy, ärsyttääkö sua, että... → does it irritate you, that...
as an irresultative object like possibly incomplete and ongoing processes: luen kirjaa→ I'm reading a book
for tentative enquiries: saanko lainata kirjaa? → can I borrow the book?
with certain pre- and postpositions: alas kohtaan varten ennen kohti vastaan ilman lähe-llä, -Itä, -lle vastapäätä keske-llä,-Itä, -Ile pitkin vasten päin ylös
When in doubt, use partitive!!
Sorry, the video may be politically incorrect for some, but still accurate.