Yes, you can! But first, you must explicitly allow for that in Tools->Options->Password by marking "Permit access by multiple users", and you need to set a password for your document. All your accounts, transactions, categories, payees, favorite reports and other important things are saved in the single file with .amj extension. Find this file on your hard drive, place it on a LAN network share or create a new LAN network share for it, so it becomes accessible from the other computers and use File->Open menu item to open it.
If LAN network share is not an option, you can use a Dropbox based solution (http://dropbox.com, free). Register with them, install DropBox on each computer where you plan to use AceMoney and DropBox will create a special directory. Every file you save there will be automatically synced up with all your computers almost instantly. So, if you entered new transactions on one computer and saved the file, you can open the file on another computer and see that change.