|You will need to create a user account on the target machine (the one with the share you want to map to) for the user(s) connecting to that share.|
For instance, let's say you logon to your PC with the following credentials:
On the target PC, create a user account with those same credentials, add that user account to the share(s) you wish to give that user account access to. Grant appropriate permissions.
The next time you logon to your PC as "joes" the drives should map automatically without requesting a password.