This tutorial does not work since 1.6 as they changed the whole way texture packs worked and made it now so you have to use resource packs instead. I'm working on a tutorial for resource packs and hope to have the video up in the next few days. Sorry for any inconvenience.
Since 13w09a, all the animated textures need a config file. To find out how to make one go to the time 7:00 in the video.
Another thing: If you're making item textures, a cheaty texture pack or just something that needs transparency then don't use paint. Use something that can save transparency and make sure the background is "erased". I only used paint in the video because I thought it would be easier to demonstrate.
In this video I show you:
How to make a normal texture pack,
How to make an animated texture pack,
How to change the config file for your textures
and how to use a video to make an animated texture pack.
In other words this video is pretty full packed (pun so intended).
How to get to the minecraft folder on a mac:
SHIFT+COMMAND+G in the finder and type in ~/library/application support/minecraft/
- Method provided by Falcon sGames
The folders you need to control click:
Download Sprite Sheet Packer: http://spritesheetpacker.codeplex.com/