As a side note to Wikia Contributors, this was made for 3.0.1c. Please update it accordingly.
Also another note, the version 3.0.1c of Thaumcraft 3 requires a version of forge that is not one of the released builds on the Minecraft Forge Forums and requires you to use the second link.
For your convenience we've written a step by step instruction on how to install Thaumcraft 3.
1: Download the required version not the latest version as sometimes the latest release of Minecraft Forge.
- For version 3.0.1c the first link will not get you the required version. The second will.
2: Download the latest version of Thaumcraft
3: In addition, you may want to consider downloading http://www.skydaz.com/damage-indicators-mod-installer-for-minecraft-1-4-6/ <~ that mod. It really helps when dealing with those pesky hell bats and angry giants.
4: Open up Minecraft.jar with 7zip or Winrar (7zip is free, Winrar is not)
5: Delete the META-INF folder.
6: Extract minecraft forge somewhere else.
7: Move all the files from the extracted minecraft forge folder into minecraft.jar
8: Close minecraft.jar
9: Run Minecraft, let Minecraft Forge do its installation.
10: Close Minecraft.
11: Go to .minecraft and put the Thaumcraft ZIP folder in the "Mods" folder.
12: Start up Minecraft. Enjoy.
13: Another easy way to do this is to go to a site called http://www.skydaz.com/. There, look up thaumcraft and follow the instructions on the page from there.(forge is automatically installed when you download from this site, so you dont have to do that pesky extracting)