That's exactly how you normally use SQL Server. Install SQL in the central server, put the database on there, then you application connects to that SQL instance.
If you don't know how to do data access in C#, there should be lots of good tutorials available on the subject
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability
We walk in the dark places no others will enter
We stand on the bridge and no one may pass