As pljvaldez suggests, su and sudo are your friends.
su or "switch user" let's you use another user's account without having to logout/login.
Type "exit" to go back to your original (login) user.
su #switches to root user (providing you have password)
su - #also switches to root user, but also loads root's environment settings (like $PATH)
su some_user #switches to user "some_user" (again, you'll need that user's password)
sudo needs to be configured by root and allows certain users, to execute certain commands as if they were root.
They won't need root's password for this. root should set up the /etc/sudoers file. Needless to say, making normal users run programs as root, can create security hazards. So use it with care.
You won't need to "exit" after sudo'ing, because sudo only let's you execute just one command.
sudo some_command #will execute "some_command" as root, if /etc/sudoers file allows it