First of all you have to go to a site that lists private servers, or go to a specific one that you like one such site is.
xtremetop100.com
Next after you find the private server you want to try/was looking for you must find the realmlist, here I selected the number one and it listed it right on the front page, you will also need to make an account and register.
Next you will then need to go to start, click My Computer, then go into your C Drive.
Start -> My Computer -> C Drive
When you go into your C:drive you will need to find your World Of Warcraft server.
You will then need to go to the "Data" folder.
When you go into the "Data" folder you will see something similar to this, you will need to select En US, or En EU depending.
When you open your En US, or Eu, folder you will need to find the Realmlist.wtf file, if this is your first time opening this you will need to:
Right Click -> Open With -> Notepad
After the first time it should just open with notepad automatically like mine.
Now you are in the Realmlist.wtf your current realmlist will be:
set realmlist us.logon.worldofwarcraft.com
set patchlist us.version.worldofwarcraft.com
set portal us
You will need to change the Set Patchlist so it will look like this :
set realmlist us.logon.worldofwarcraft.com
set patchlist (insert private server patchlist here)
set portal us
To go back to retail WoW you will just need to change the patchlist back.
In my Photo showing the patchlist I have both ways shown- you do NOT put both ways in the Realmlist just change the patchlist, i just did this to show.
You now know how to enter a WoW Private Server

! Gratz.