Learn Russian: Все звёзды больше, чем наша планета.

Все is the plural form of the pronoun for "all", which we need here to match the plural noun звёзды (stars). If you used всё, it would mean "everything" or would be used to modify a neuter singular noun.

I learned the word for star is звезда. Where did the ё come from in звёзды?

The stress moves when making this word plural. The singular is звезда with the stress on the last syllable. The plural is звёзды with the stress on the first syllable. In Russian, when the stress shifts onto certain е vowels, they change to a ё sound.

How does the comparison word чем work here?

Чем translates to "than" when comparing things. When you use чем, the second thing being compared (наша планета) stays in the Nominative case, which is just its basic dictionary form.

Is there another way to say this without using чем?

Yes! Another very common way to compare things in Russian is to drop чем and change the second item into the Genitive case. So, you could also say Все звёзды больше нашей планеты. Both ways are perfectly correct.