As jhu said:
1. Set up user with no extra group memberships. (ie, only a member if its own private group)
2. remove "other" access to everything (can't vouch that this wont break anything). effective, everything becomes 770 or 750. If you want to ensure they cannot get a shell on the machine, change their line in /etc/passwd from /bin/bash to /sbin/nologin or /bin/null.
If all you want is to ensure that they cant EDIT the other stuff, then just make sure noone other than you/ appropriate owner has write access.
Newbies remember, the numbers are made up by adding: read (4) write (2) and execute (1). So, if I had read and write, but not execute, it is 6. read and execute, but not write = 5. everything = 7. and first number is owner, then group, then others.