There are different ways to deal with permissions problems and elevated privileges, each with its advantages and weaknesses. …
Add user to group
Add a user to a group that has needed privileges. You can do this from the terminal, or use a GUI tool like Webmin. Log out and back in after doing so so that /etc/passwd and /etc/group are read again. Once done, then the user will have the privileges of the group.
For example, consider the imaginary command /usr/sbin/foo which normally needs to be run as root. You, the system administrator, want to allow user bar to run it, but you don't want to give the user the root password or let all users run foo (as would happen if you set foo suid root). Instead, see what group the file /usr/sbin/foo belongs to, and add user bar to that group.
This is a fine-grained, per-user way of dealing with permissions. You can also create a group with particular permissions for your needs. Just don't add anyone to the group root.
suid is an access rights flag that allows users to run an executable with the permissions of the executable's owner, usually root. It allows all users to perform one specific task that requires root privileges without having to know the root password.
As root, it is easy to set up. For example, to make hddtemp suid root:
# chmod u+s /usr/sbin/hddtemp
All users can run such a command with full root privileges, so this is not a fine grained tool. Do not use it thoughtlessly.
By editing the /etc/sudoers file you can achieve something similar to a fine grained suid root. You can allow a particular user or group run a particular executable without having to provide a password. One example is here.
TODO: Find out more about this. PAM seems to be popular on Debian based distributions. One reference is found here. On Linux Mint Debian Edition, PAM's configuration files are found at /etc/pam.d. Webmin has a PAM module (System – PAM Authentication); like other Webmin modules, it presupposes the user is familiar with the material.
TODO: Find out more about this. PoilicyKit seems to be popular on Red Hat based distributions.