Learn Finnish: Tämä on tuoli.

Finnish does not have articles like 'a', 'an', or 'the'. The word tuoli can mean 'a chair' or 'the chair' depending on the context. Here, the phrase naturally translates to 'This is a chair.'

Why do we use tämä instead of tuo or se?

Tämä means 'this' and is used for something right here, close to the speaker. Tuo means 'that' (something further away but you can still point to it), and se usually means 'it' or 'that' when referring to something out of sight or previously mentioned. Since you are talking about a chair right in front of you, you use tämä.

Could I just say On tuoli and drop the word tämä?

No, you need to keep tämä. In Finnish, you can often drop the pronouns for 'I' (minä) or 'you' (sinä) because the verb ending already tells you who is doing the action. But for third-person words like 'he', 'she', 'it', or 'this' (tämä), you must keep the pronoun in the sentence so people know what you are talking about.

Why is the word tuoli in its basic dictionary form here?

When you use the verb olla (to be) to say what a single, whole, concrete thing is, the noun following it stays in its basic dictionary form (called the nominative case). Since we are simply identifying one whole chair, tuoli does not need any special endings.