How do I create bootable USB media so that when I power on the computer, it finds Windows Server 2016 setup.exe?

If you have the iso you can also use the refus boot tool to create a bootable flash drive from the iso....   The following webpage give you instruction on how to use the tool and a place to download it as well. It is quick and very easy to use.... it works faster than some of the other tools as well it is a portable ap which means it does not install on the computer you just run it from the download.  https://rufus.ie/

You do not need to download tools to create a bootable  USB drive using Windows command prompt ( CMD ).

To Create bootable USB for windows 7/8/10/2008/2012/2016
1- You need to run an elevated command prompt. Start | type cmd | Right-click cmd (top of menu) | Run as Administrator
2- Next you will run Diskpart to prepare the disk for the OS   {question mark “?” below should be replaced with the disk number of the drive you are using}
•      diskpart
•      list disk
•      select disk ?
•      clean
•      create partition primary
•      select partition 1
•      active
•      format fs=ntfs quick label=”Win8-RP-x64”
•      ASSIGN- Assigns a drive letter.
•      exit
Leaving DiskPart...
3- Now we need to copy the boot sector.  You should still be in the command prompt window
•      g:
•      cd boot
•      bootsect /nt60 g:
•      exit
•      xcopy g:\*.* h:\ /E /H /F    where g: is CD Drive, h: USB drive
exit the command prompt then make sure boot from USB option on the computer BIOS is on the top of the booting list.

the link below shows the full tutorial
https://www.dell.com/support/article/us/en/04/sln153364/create-a-bootable-usb-flash-drive-using-the-diskpart-utility?lang=en#Create

Thats a lot of work..... it is easier and faster to use a usb creating tool especially using a portable ap such as rufus, that does not install the app is quite small and downloads in seconds. You can do it the manual way but it is more difficult.

i agree with  "a lot of work" a bit, but at least you know what you did, and what failed, if it fails at all.
it also educates you abit.
i have used disk part several times; and i like using it
 i have used the windows Mediacreator tool also, and it works well - that should be my first choice here !

Thank you for the variety of ways to create a bootable usb!  I am learning from you experts and appreciate your help.

Please note, that what you selected as solution (USB download tool), will not work on many types of hardware, since it always formats as NTFS.

UPDATE:

In regard to McKnife's comments:  "I suggest you simply try it with NTFS and if you don't succeed . . ."

I tried to boot / install Windows Server 2016 Server from a USB (NTFS) on the new computer, but it did not work.  McKinfe is correct, the new computer has a UEFI BIOS.

I then used McKnife's solution:  "you use this software: http://www.winsetupfromusb.com/downloads/ which allows splitting. I will add a picture about how to configure it. It will work anywhere."

I downloaded the software, followed the instructions in McKnife's image above, and added the path to the Window Server 2016 ISO file.  The software created the USB boot files and split the Windows Server 2016 ISO file.

I placed the USB in the new computer and powered it on . . . The next message to appear:  Welcome to Windows Server 2016, click OK to install.

I will need to try that next time, thanks for the feedback and fairly distributing the points.

You're welcome Web_Tracker.  I had never heard of UEFI BIOS until McKnife mentioned it.