The quick and simple way to do this is as follows:
On your domain controller make sure the follwoing folder is shared already:
c:\WINDOWS\SYSVOL\domain\scripts
This folder should show up as 'NETLOGON' if you browse the server name. This is where you need to stick your logon batch files.
Then simply open up a users acount in Active Directory Users and Computers on the server. Go to the profile tab and in the 'Logon Script' box type the name of the batch file you want to use from the netlogon folder i.e mylogon.bat
The user should automatically run the logon script next time they log in to the PC.
Alternatively you can use active directory scripting, but if you just wanna map drives for now, stick with the above method.
Like heropsycho2177 said though, do some reading on GPOs and you'll find you can do an immense amount of things automatically and easily.