Advice for a windows XP computer, with NTFS file system. Also, I suppose those computers are not in a Windows domain, they are in a workgroup, as you said. Pay attention, these are technical terms (windows domain and workgroup; if you have your computers in a bigger enterprise network you will better talk to your network administrator).
Create those users, with the same password, on the system where the share lies
(this is a solution, there are more). Create share, give rights to those users to that share. There are sharing security settings and file security settings... You have to play with both.
Other solution, close to first (I have not played for long with such things, I do not know if I am right... You tell me, ok?):
You don't create those users on the computer with the share. You will grant them the right to "Access this computer from the network" (Start->Control Panel->Administrative Tools->Local Security Policy->User Rights Assignments), mentioning the usernames like: computername\username (username=user account; computername = the name of the computer on the network on which that user account is defined and not the computer which has the share). You will grant them access to share (right click on folder, "sharing and security") using the same method (mention the user as computername\username). Be carefull to: grant access for share, disable "guest" account on the computer with the share, do not give the local group "Everyone" access to that share (but do not forbidd the access of the group "Everyone" to that folder, just erase the group from the list when you are granting access rights.
Tell us which one you choose.