The answer is different in theory than it is in reality, but lets start with the theory first.
The network ca never practically be slit perfectly evenly, even if it is as more computing power is added to the problem one side will "win out" and the blockchain, by definition, is officially the longest (most complex) chain yet mined. So eventually the losing side would be undone, as if it never happened (within the scope of the blockchain... goods or services would still have been exchanged).
That assumes that all of the nodes are independent and operating following a basic set of rules and weren't rational beings. What would happen in reality is that the largest mining pools would panic very quickly. Likely they would suspend mining operations in some fashion, likely keeping the workers "busy" with bogus information and throwing away the work. What this would do is drop the hashrate of the network. Assuming coordination (or at least rational action) among the vast majority of the mining effort once the split was resolved (say a treaty was signed) the major operations would resume normal operations.
In their absence the chain would, at first, flounder, not mining any new blocks until the difficulty was re-adjusted for the now lowered hashrate. Once they came back online in a coordinated way blocks would be mined very quickly, potentially fragmenting the network until, again, the hashrate was adjusted back up. At this point the algorthim takes over and the chain with the most amount of work would win and all the other chains would disapear. This would be very controlled, however, and since the largest pools would be in a position to advertise the split and warn people very little would be lost in terms of bitcoin transactions disappearing. Mostly it would damage the reputation of bitcoin.
A slightly alternative scenario to this is that the pools suspend operations only long enough to determine who is on the larger side of the split, then resume. This would be nearly seamless to everyone on the winning side and hardly harm the reputation of bitcoin since it, along with many other services, could point to the great Internet split and blame that unfathomable one time event.