How to connect Apple laptop to Windows drive (SMB)

To map a windows drive on a Mac laptop:  (from Apple)

smb://DOMAIN;User@ServerName/ShareName

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A bit easier to remember:

On the Mac, from Finder's GO menu, choose "Connect to Server" 
Enter the server address, preceded by smb://, as shown:

You'll get prompted to enter your network credentials - need to add the Windows DOMAIN\user_name for the Name Field:

What is SMB?
SMB, which stands for Server Message Block, is a protocol for sharing files, printers, serial ports, and communications abstractions such as named pipes and mail slots between computers.

Early document on it is a Microsoft/Intel document called Microsoft Networks/OpenNET-FILE SHARING PROTOCOL from 1987. The protocol was subsequently developed further by Microsoft and others. Many of the documents that define the SMB protocol(s) are available at ftp.microsoft.com in the SMB documentation area.