How old is the version of Slackware you're talking about?
As long as the users are the owners of their own home directories, they should have no trouble writing to them.
I'm assuming you used `adduser` to create the users for that system. I don't add users very often, so I don't recall if it automatically creates a home directory for them. If not, just do so as root and use `chown` to change the owner of that directory to the user in question. (In case you don't know, it should be in /home/<userid>.) I would also change the group while you're at it.
chown <userid>:users /home/<userid>
I don't think you have to make it writable, but in case you do...
chmod 744 /home/<userid>
This makes their home directories also readable by others. Use 700 if you want to give them exclusive access to that folder.
man adduser, chown and chmod for more info...