How Does the Typical Paper Money Transaction Occur?

Most paper money dealers don't have stores in the same sense as coin dealers. Most transactions occur through the mail and over the phone. It may seem less than ideal initially, but it works very well. Nearly every dealer who works through the mail offers a money-back, no-questions-asked policy. If the note you buy is not really the one you want, you can almost always return it. Typically, collectors will use an adequate reference book to find the note they want. Then, they look through the many price lists they might have to find a dealer who offers the same note in an acceptable condition for an acceptable price. The collector then either calls or faxes the dealer with a credit card number or sends a check in the mail.
The next most typical transaction occurs at paper money and coin shows. Shows are also a good way to learn about notes and the hobby in general.

Another type of transaction is where a collector sends notes to a dealer who may then buy them or return them. It's best to ask the dealer first with the list of notes you plan to send. This is an acceptable and safe way to do business as long as the dealer is reputable (membership in PCDA or IBNS is a good reference as dealers can and do get thrown out for violations).
Yet another type of transaction is the mail auction where collectors all put up their notes for auction (usually through the mail) and then a list of notes is sent out to a large group of people who bid on the notes through the mail. Thousands of notes are auctioned this way. The IBNS has regular auctions with about 2000 lots per auction and minimum bids starting at 2 US dollars per lot: clearly an auction for regular collectors.

When buying notes, avoid notes that have been cleaned, patched, ironed or otherwise "fixed up" to improve the looks. Be careful of notes that have missing details, serial number digits, etc. They may have been removed with an electric eraser.