Learn Finnish: Tämä on koira.

Finnish does not have articles like "a", "an", or "the". The word koira can mean either "a dog" or "the dog" depending on the context. In this sentence, "a dog" is the natural English translation.

What is the difference between tämä and other pointing words?

tämä means "this" and is used for something very close to the speaker. If the dog were further away, you would use tuo (that over there) or se (it/that).

Is on the standard word for "is"?

Yes, on is the "he/she/it is" form of the verb olla (to be). You will use on anytime you use tämä, tuo, or se to identify a single thing.

Why is koira in its basic dictionary form here?

When you use a sentence to simply identify what something is (like "This is a dog"), the noun stays in its basic form, which is called the nominative case.