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Windows (names and instructions may vary depending on your version of Windows):
1: Download WinRAR (http://goo.gl/XHHRZ) or 7-Zip (http://goo.gl/TgWmU) (this tutorial will be using WinRAR,

2: navigate to %APPDATA%/.minecraft/bin to loacate the "minecraft.jar" file,

3: right click minecraft.jar and select "open with" then "WinRAR Archiver"

4: once inside minecraft.jar, drag all the .class files included with ExtraBiomes into minecraft.jar. Click OK.

5: Delete the META-INF folder within minecraft.jar to avoid the black screen of doom.

6: Play Minecraft.
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Mac:
1: Copy and paste the following code EXACTLY into Terminal.app (you should find it through spotlight, or the Utilities folder located in Applications):

cd ~
mkdir mctmp
cd mctmp
jar xf ~/Library/Application\ Support/minecraft/bin/minecraft.jar

This code will create a folder in your home directory called "mctp", navigate to that new folder now.

2: Once in "mctp" drag all the .class files included with the ExtraBiomes download into the mctp folder. When it askes you if you want to replace a file, check "Apply to all" and "replace".

3: Then copy and paste the following code into your terminal EXACTLY as I say:

rm META-INF/MOJANG_C.*
jar uf ~/Library/Application\ Support/minecraft/bin/minecraft.jar ./
cd ..
rm -rf mctmp

This code will apply the mod to minecraft.jar and automatically delete the META-INF folder for you.

4: Run Minecraft.
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If you have any further questions or problems regarding installation, feel free to ask in the forum page at: 'http://goo.gl/nGV11'

Mac instructions supplied by Risugami, thanks!