Step1
Download or install the game client. If you have already installed the game client from a retail version, go to step 2. If not, then you will need to download it. There are several places to get it, but the most reliable place is from the World of Warcraft website. Here is the url: http://www.worldofwarcraft.com/account/download_wow.html
Install the game, but do not run it yet. If you have not purchased an account, it will not work anyway......yet!
Step2
Now you need to get access to a private server. There are tons of them, so if you don't like the first one that you pick, there are thousands more.
The easiest way to find them, is to use a search engine. Type "wow free server" or "free wow server" in the text box and begin your search.
Step3
You will be given a long list of the best results. If you are using google, click the first one, which will be "World of Warcraft top 100 - Private servers, Guides, Guilds, free ..."
All of the first few results will be websites that contain top 100 lists of free private servers. Any of these will work to find a server that suits your play style. Click one of them to get a list.
Step4
Now you should have a list of the top 100 free servers. View the descriptions of each one. The descriptions are often abbreviated or contain words like "blizzlike" or "2.4.x support". Blizzlike is a term that the servers use to state that the experience gained is the same or very similar to the pay-to-play game. 2.4.x refers to the patch version. Some servers do not require you to update to the current patch in order to play. These servers may not work if you have the current patch installed. A GM is a moderator (a live humaan being that monitors player interaction to help with bugs or to assist in keeping the swearing, harrassment, etc. to a minimum. A server with active GM's is preferred for most people.
Step5
Now, you will need to choose one of these servers. Some have an installer to download that will change your realmlist file for you and have its own game launcher. Do not be afraid to download these, but you should always scan them for viruses/malware anyway. Some servers will not require you to download anything, so you will have to change your realmlist file manually.
It is an easy process, and ALL of the servers will give you instructions on how to do this.
All private servers require you to create an account. All you need is a valid email address. Just create a username and password, and you will be sent an email with a verification link in it. Click on the link in your email to activate your account. It takes between 2 and 15 minutes for the server to activate the account, so be patient.
ALWAYS make a backup of your "realmlist.wtf" file BEFORE you make changes to it. If you do not, you will have problems connecting to the game if you want to use the official version. To make a backup, you can simply rename the file. Ex.: "realmlist_original.wtf"
Once your registration is made active, and your realmlist file is edited correctly, you may begin pwning noobs! Be careful, and don't get too cocky if you chose a server with an instant level 70 with epics, some servers have been up for years, so your epics may be useless in pvp.
Enjoy!