I know I need to have a primary key set, and to set anything that should be unique as a unique key, but what is an INDEX and how do I use them?
What are the benefits
The easiest way to think about an index is to think about a dictionary. It has words and it has definitions corresponding to those words. The dictionary has an index on "word" because when you go to a dictionary you want to look up a word quickly, then get its definition. A dictionary usually contains just one index - an index by word.
A database is analogous. When you have a bunch of data in the database, you will have certain ways that you want to get it out. Let's say you have a User table and you often look up a user by the FirstName column. Since this is an operation that you are doing often in your application, you should consider using an index on this column. That will create a structure in the database that is sorted, if you will, by that column, so that looking up something by first name is like looking up a word in a dictionary. If you didn't have this index you might need to look at ALL rows before you determine which ones have a specific FirstName. By adding an index, you have made this fast.
So why not put an index on all columns and make them all fast? Like everything, there is a trade off. Every time you insert a row into the table User, the database will need to perform its magic and sort everything on your indexed column. This can be expensive.