IMac – What are the OS X Mavericks hardware system requirements

You can check out the directions on iFixit here.
There are a lot of steps, but none of it is really rocket science. They explain it in detail.

My bigger question would be whether the two boards are compatible.
Based on the specs for each one (2,1 / 3,1), the main differences are (respectively):

• Processor: TS7400 / TS7500
  
• Video Card (integrated): Intel GMA 950 / IntelGMA X3100
  
• VRAM: 64MB / 144MB

I'm not sure how these effect logic board compatibility, but I'd be careful.

Also worth noting that the white 3,1 actually supports 6GB of memory (unofficially). Get it here.

Hope this helps.

Upgrading to Lion or Mountain Lion would not improve your Mac's performance. It may actually decrease performance as the newer versions of Mac OS X seem to require/want more RAM to run smoothly. Apple has increased the minimum amount of RAM in almost all of their line up to deal with this issue.

You currently only have 1GB of RAM... upgrading this would probably be the cheapest and most efficient method of speeding up your Mac. Freezing and unresponsiveness can be caused by lack of RAM.

Check out this Apple support article that will teach you how to use OS X's Activity Monitor to check whether RAM would improve performance.

After determining whether or not you need more RAM (you do!), you can find out what kind by following these steps:

1. Click the  in the Menu Bar
2. Click "About This Mac"
3. Click "More Info..." in the About This Mac dialog box

4. Click on the "Memory" tab

   • Listed will be what type of memory you have and how much. In the lower right hand corner is a link to "Memory Upgrade Instructions" — follow these instructions.