For this to work, both computers need to have access to a common hard drive so you can put the Pedia folder in a public folder. To simplify this how-to, we'll call the two computers one and two.
1) Make sure the Pedia program is not running. Then move the data folder, by default located in your Home folder under User/Library/Application Support/[Name of the Pedia], to the desired new location.
2) Then hold down the option key and start up the Pedia program on computer one. This will prompt you to choose a database. Choose the data folder you just moved to the new location.
How to share a library between two computers
3) Now do the same with computer two and choose the same folder that computer one is using.
NOTE: If you ever forget where you have put the data folder, you can see the path in Preferences/General.