|This should get you started...|
The first thing you have to do is Unlock all cells that you want users to enter data into.
In order to lock a specific range, you must protect the entire sheet. By Unlocking certain ranges, the sheet can be protected but users can still enter data where you want them to. For example, if the only range you are trying to protect is Column B, then Unlock every Column except for B.
Right click the sheet tab for the sheet you want this to work in and paste this code into the pane that opens. Note that the password is set to zzzzz. You can change that to whatever you want the password to be.
Private Sub Worksheet_Change(ByVal Target As Range)
'Determine if change was made to Column A
If Target.Column = 1 Then
'Unprotect Sheet, Enter Date/Time in Column B, Protect sheet
Cells(Target.Row, 2) = Now
Please note that unless you hide and password protect the VBA code itself, users will be able to see it, change it, find the password, etc. See here for the instructions on how to protect the code:
Click Here Before Posting Data or VBA Code ---> How To Post Data or Code.