How do I copy a file/folder from another user's home directory in Linux?

If you don't have permission, then you can't copy the file.

The only ways around that are by elevating your permissions, for example by becoming root or the other user. You could try 'scp':

scp other_user@localhost:file .

or copy the file as root (but then be aware that the destination file is owned by root).

The other user either needs to give you read access (and execute access on the directories).

You can most repeatably do this by creating a group and having both of you join it, then granting appropriate access to the group.

You can also copy the file as root, if it's one-time, then use chown/chgrp to reset the permissions to your user.

(It may also be easier to request the other user copy the file into a folder you set up.)