<p>What are the different types of indexes, what are the benefits of each?</p>

<p>I heard of covering and clustered indexes, are there more? Where would you use them?</p>

OdeToCode has a good article covering the basic differences
As it says in the article:
Proper indexes are crucial for good
  performance in large databases.
  Sometimes you can make up for a poorly
  written query with a good index, but
  it can be hard to make up for poor
  indexing with even the best queries.
Quite true, too... If you're just starting out with it, I'd focus on clustered and composite indexes, since they'll probably be what you use the most.