Learn German: Ich glaube, dass sie ein hässliches Sofa kauft. - I think that she is buying an ugly sofa.

Sofa is a neuter noun (das Sofa). In this sentence, it is the direct object being bought, so it takes the accusative case. When an adjective comes after the indefinite article ein for a neuter noun in the accusative case, we must add the ending -es.

Why is the verb kauft at the very end of the sentence?

The word dass (that) is a connecting word that starts a subordinate clause. In German, these types of words force the conjugated verb (in this case, kauft) to move to the very end of that part of the sentence.

Is the comma before dass strictly necessary?

Yes, it is mandatory! Unlike in English, where a comma before 'that' is usually wrong, German punctuation rules require a comma to separate the main clause (Ich glaube) from a dependent clause starting with dass.

How can I tell that sie means 'she' and not 'they' here?

You can tell by looking at the verb ending. The verb is kauft, which ends in -t. This matches the third-person singular (he/she/it). If it meant 'they', the verb would be kaufen.