Learn Finnish: Tämä koira on täällä, ja nuo kissat ovat tuolla. - This dog is here, and those cats are there.

In Finnish, the pointing word (demonstrative pronoun) must match the noun it describes. Because kissat (cats) is plural, as shown by the -t at the end, you must use the plural word nuo (those) instead of the singular tuo (that).

Why does the verb change from on to ovat in the second half of the sentence?

on is the singular form meaning 'is', used for one dog (tämä koira). ovat is the plural form meaning 'are', used because there are multiple cats (nuo kissat). Just like in English, the verb must match whether the subject is singular or plural.

I learned that ne means 'they' or 'those'. Could I say ne kissat here instead of nuo kissat?

You could, but it changes the meaning slightly. nuo means 'those' when you are pointing at things you can actually see right now in the distance. ne is generally used as 'those' for things you cannot see or things you were just talking about in a previous sentence.

How do täällä and tuolla relate to the other words in the sentence?

They are location words built from the same ideas as the pointing words. täällä (here) shares a root with tämä (this), referring to a place close to the speaker. tuolla (there or over there) shares a root with tuo (that) and nuo (those), pointing to a place further away.