1. You create a function in your application that maps a customer id to a database server. There is only one at first.
2. You setup replication to another server.
3. You update your application's mapping function to map about half of your ids to the new replica. Use something like md5(customer id) % 2. Using md5 or something else that has a good random distribution is important (sha-x DOES NOT have a good random distribution).
4. You application now will write to the replica, turn off replication, and delete the ids from each server that no longer map to that server.
Adding a new server follows approximately the same lines, except you need to rebalance your keys which can be tricky.