How big is each LAN, and what kind of hardware are you using?? Do you use Cisco hardware, or just SOHO type hardware, like Linksys to create each LAN?
You COULD connect them through VPN over the internet, or you could get a Frame Relay / ATM Circuit to connect the two...
Over the internet would be cheaper, however, response time on an internet connection will be higher than that of a dedicated circuit.
Then you have to deciede with each method, there is a possibility that you may have downtime.... if the internet goes down, or if the dedicated circuit has troubles, both offices will be completly cut off from one another... perhaps an ISDN line configured to be dialed when the main link drops would be a good idea.
What kind of traffic will there be going between the LAN's? Just data files, VOIP calls between the offices?