How ON EARTH do I install BF3 on PC?

This simpliest way to install BF3 on your PC if you are receiving errors during an attempted installation from physical media is to redeem your CD key in origin.  This will give you a digital copy of the game and bypass any errors that you get while installing from disc. 

To do this log into your PC origin client, click the "origin" menu in the top left hand corner, then click on "redeem product code" and enter your BF3 CD key.  After BF3 installs, if you have purchased BF3 premium or any stand alone expansion packs right click the BF3 icon in your games library and select "show game details" then on each expansion right click and select "download".  After all selected expansions download you can play BF3 on the expansion packs. Then go to Battlelog, multiplayer, server browser and at the top of the page add the new expansion maps and game modes to your server browser filter settings to find games on the new maps.

Since you didn't list your PC specs here are the minimum and recommended PC specs to play BF3.  Please keep in mind that BF3 is a resource instensive game and many PCs are incapable of running it:

Minimum requirements for Battlefield 3

• OS: Windows Vista or Windows 7
• Processor: Core 2 Duo 2.4 GHz or Althon X2 2.7 GHz
• RAM: 2GB
• Graphic card: DirectX 10 or 11 compatible Nvidia or AMD ATI card, ATI Radeon 3870 or higher, Nvidia GeForce 8800 GT or higher.
• Graphics card memory: 512 MB
• Sound card: DirectX compatibl sound card
• Hard drive: 15 GB for disc version or 10 GB for digital version

Recommended system requirements for Battlefield 3

• OS: Windows 7 64-bit
• Processor: Quad-core Intel or AMD CPU
• RAM: 4GB
• Graphics card: DirectX 11 Nvidia or AMD ATI card, Nvidia GeForce GTX 560 or ATI Radeon 6950.
• Graphics card memory: 1 GB
• Sound card: DirectX compatibl sound card
• Hard drive: 15 GB for disc version or 10 GB for digital version