The best single tip on using hashes for me was a bit in Programming Perl (2nd ed, it is in the 3rd as well) about how to translate Perl data structures into English.

A hash lookup is the word "of".

So, for instance, if you want to be able to find the address of a person, you would name the hash %address, make the keys be the $name of the person, and addess the address with:

print "$name has an address of $address{$name}\n";
[download]

(Read the hash lookup as, "address of $name".)

I find this little tip to be very useful in figuring out where you can use hashes, what to call them, and how to read code written with them. After that take a look in the Cookbook for some of the hash tricks, and as you read them see how they fit in this mental model. The answer generally is, "Pretty well."