How to upgrade processor on 2009 education only iMac.

Sorry your only choice is to replace the complete logic board. Here's the needed logic board: iMac Alu 20" Logic Board, 2.0GHz (Edu) Apple P/N 661-5193 or if you live in the states: iMac Alu 20" Logic Board, 2.0GHz (Edu) Apple P/N 661-5193 As you can see its not too expensive less than $200 US.

Here's the IFIXIT guide you'll need to follow: iMac Intel 20" EMC 2266 Logic Board Replacement

Now do keep in mind this is a Core 2 Duo based system and Apple no longer supports it with the newer MacOS's El Capitan is the last OS this system will run. You may want to think long and hard before you spend any money on fixing this system if you think you'll want to get any newer apps. It might be wise to put the money towards a newer system (used or new).