Learn Polish: To jest lepszy pomysł. - This is a better idea.

You don't! Just like in English, where the word 'good' completely changes to 'better', the Polish comparative for dobry is completely irregular. You simply have to memorize that lepszy is the word for better.

Why does lepszy end in -y in this sentence?

Even in their comparative forms, adjectives still have to match the gender of the noun they describe. Because pomysł is a masculine noun, we use the masculine ending -y. If you were describing a feminine noun, you would use lepsza.

Doesn't the verb jest usually force the next noun into the Instrumental case? Why is pomysł in the basic Nominative case?

When a sentence uses the specific structure to jest (this is) to point something out, the noun phrase that follows stays in the basic Nominative case. You only use the Instrumental case if you start with a regular subject pronoun describing someone's identity or profession, like in On jest dobrym człowiekiem (He is a good person).

Can I drop the word jest in this sentence?

Yes, saying To lepszy pomysł is very common in everyday Polish. It means exactly the same thing but sounds a bit more natural and casual in conversation.