We just replaced the alternator on my car and the battery fuse in the engine and now the service engine soon light is on. What could the problems be?

Attach a scan tool or code reader to the Data Link Connector, located under the dash, if the Check Engine Light is on. You might want to disconnect the negative battery cable for 15 seconds, first, to try and reset the ECM. If it is truly a Service Engine Light, you may need to change your oil. Consult your Owner's Manual for how to reset.

Something may have been left disconnected when the car was put back together; it could also just be a coincidence that the light came on right after the car was serviced. Like tx asked, is it a maintenance light or is it actually the service engine light? That will make a difference.

If it's not a maintenance light, then you do need to check for codes, like tx said; however, disconnecting the battery will not reset the computer. The computer is running on an OBD-II system which needs to be manually reset with a diagnostic scanner.