Instructions
Download the most recent "World of Warcraft" update from your desired patch mirror website. Blizzard Support links to three different pages, though more exist. Each patch has two separate files you must download: a .tfil and an .mpq. Depending on the website from which you download them, the two files may be bundled in a compressed archive.
Open the folder where you chose to download the patch files. Right-click the file and click "Extract Here" if the file is a ZIP or RAR file.
Open your "World of Warcraft" installation folder in a separate window. This folder was specified when you installed the game. By default, the game is in the "C:/Program Files (x86)" folder.
Drag the .tfil file into the main "World of Warcraft" installation folder.
Double-click the "Data" folder in your "World of Warcraft" installation folder.
Drag the .mpq file into the "Data" folder.
Open the "World of Warcraft" launcher as normal. Instead of having to download the patches from its own servers, the launcher will install what you just placed into its folders, cutting down on the patching time significantly. The "Play" button will reactivate when it is done patching.