Learn Finnish: Pöydällä on jauhoa. - There is flour on the table.

This is an existential sentence introducing a mass noun (a substance you cannot easily count, like flour or water). When saying "there is some [substance]" in a location, Finnish uses the partitive case for the subject to show it is an unspecified, open-ended amount.

Why doesn't the sentence use a word for "there", like "Siellä on jauhoa pöydällä"?

Finnish doesn't use a filler subject like the English "there". Instead, an existential sentence simply starts with the location (Pöydällä), followed by the verb (on), and ends with the new thing being introduced (jauhoa).

If there were multiple things on the table, would the verb change to ovat?

No, in these "location first" existential clauses, the verb is always locked to the 3rd person singular (on). Even if the subject is plural, like Pöydällä on omenoita (There are apples on the table), the verb remains singular.

I remember the word for table is pöytä. Why does the t change to a d in pöydällä?

This is a classic example of consonant gradation. Adding the adessive ending -llä (on) closes the final syllable. This forces the strong consonant t in pöytä to weaken to d, resulting in pöydällä.