How do I run sudo command from standard account? From what I've read, it is good security approach to have two accounts, one admin and one standard.

I am trying to run the following command in terminal on my standard account

sudo mv /System/Library/CoreServices/Search.bundle /System/Library/CoreServices/Search.bundle.bak killall SystemUIServer


It asks for a password at which point the process fails because the current user "is not in the sudoers file."

Is it asking for my admin account password or root password?  Do I have a root account/password if I haven't explicitly set one up? How do I temporarily elevate my access to execute the command without necessarily enabling root?
The system is asking for the password of your account and then verifies whether you are allowed to run sudo based on the content of /etc/sudoers. By default only Administrators (which have the option ticket in Preferences) are allowed to do this.

In case you want to run shell commands with sudo without having to switch users all the time you have several options:


Use ssh &lt;any-admin-user&gt;@localhost to log in as an admin user and run sudo then 
Add your non-admin user to /etc/sudoers by logging in as an admin user, executing sudo visudo in Terminal, duplicating the %admin    ALL=(ALL) ALL line and replacing %admin with your username. This will allow you to use sudo in Terminal without giving you full admin access. Using visudo instead of editing the file directly will ensure that the file gets checked for syntactical correctness on save (an error in /etc/sudoers might lock you out of your system completely)