How do I run sudo command from standard account?

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 <any-admin-user>@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)

I answered a similar question here

Seems like you could use the SU command to switch to another user in Terminal. Once you've switched to the admin user you can use sudo commands coupled with the admin account's password.

For example, when I'm at one of my end user's Macs and I need to run something with elevated privileges (chown for example) without logging out and into the admin account (ladmin) I would use something like this (in bold):

Mr-Rabbits-Mac:~ notadminuser$ su ladmin

This will prompt for the ladmin account's password, once entered you will see a bash command prompt. From here I can run any sudo commands desired, entering ladmin's password as needed...

bash-3.2$ sudo chown user2 /some/folder

This will run the chown command using the now logged in ladmin user, prompting for the ladmin account's password. Once finished you can type exit to return to your logged in user's prompt.

Screenshot of similar process, only using sudo to run the ls command (just for example).