Wow, that's just such a huge topic, it's hard to answer in this format. I srtongly recommend this book.
Relational Database Index Design and the Optimizers
by Tapio Lahdenmaki
You don't just use indexes to make table access faster, sometimes you make indexes to avoid table access altogether. Something not mentioned yet but vital.
There's a whole science to this if you really want to make your database perform maximally.
Ah, one specific optimization to Oracle is building reverse key indexes. If you have a PK index of a monoatomically increasing value, like a sequence, and you have highly concurrent inserts and don't plan to range scan that column then make it a reverse key index.
See how specific these optimizations can be?