Learn Finnish: Minä tarvitsen munia ja maitoa.

Munia is the partitive plural of muna (egg). You use the plural here because you need multiple whole eggs. The ending -ia is added to the base word muna to make it plural partitive. If you said munaa (partitive singular), it would mean you need a piece of an egg or some egg as a mass ingredient.

Why is maitoa in the partitive singular instead of the partitive plural?

Maito (milk) is an uncountable mass noun, just like water or coffee. Because you cannot easily count individual milks, you use the partitive singular maitoa to mean "some milk". Eggs are countable, so they get the partitive plural munia.

Why do we use the partitive case for the objects of tarvitsen here?

The verb tarvita (to need) takes the partitive case when the object is an indefinite amount. Because you are expressing a need for "some" eggs and "some" milk rather than a specific, limited quantity (like "those specific eggs"), both nouns take the partitive.

The dictionary form is tarvita, so why does it change to tarvitsen?