So you have installed MS-SQL on a network server and it all runs fine there.
But, you cannot get a connection to the SQL Engine from any of the network client PCs.

There are several thing to look at.

1: From the Server, running SQL Management Studio, right click the SERVER Instance you want to connect to and check its properties – Connections and make sure you have this checked…
  [x] Allow remote connections to this server.  

If that is checked, then the next step is to start the MS SQL Server Configuration Manager.
Then look at the SQL Server Services.
If you see an error message [   The remote procedure call failed. [0x800706be]   ]as shown below then you may be running SQL2008 R1 version. Updating it to patch R2 should fix the RPC problem (UNLESS you have also installed a later SQL version.)

rpc failed error message

rpc failed

If you have SQL2008 R2 installed and also a later SQLServer version, then you need update to SQL Server 2008 SP3 or later.

Or try using the MS SQL Server Configuration Manager from the later edition.

Once you have the MS SQL Server Configuration Manager running, set the SQL Server Browser StartMode to Automatic.

By default, it is set Disabled.

Next, start the service.

server browser setting

set the Browser running

Now try again to have the client PCs connect, and if you have User Permissions correct, your networked PCs should now see the database.

  John Griffiths