You don't need to map a drive. What you need to do is:
1) Ensure that both machines are members of the same workgroup.
2) At machine A:
3) right-click a folder and choose Sharing And Security
4) Check the box "Share this folder on the newtwork"
5) Optionally, check the box "Allow network users to change my files.
6)Repeat for any other folders that you want to share on this machine.
7) At machine B:
Repeat steps 3- 6 as required
How you access the files will depend on the Operating system of the machine that you want to access them from. You haven't told us what Operating system is on either of the machines.