How do I transfer from old mac mini to new using same monitor and keyboard

To transfer user data and files from the Mac mini to a new Mac, use Time Machine to create a backup of the mini to an external drive. When you get your new Mac, connect that TM backup drive to the new Mac, along with the keyboard and mouse and use the Setup Assistant or Migration Assistant app to transfer your data.

Please see > Back up your Mac with Time Machine - Apple Support

and see > Move your content to a new Mac - Apple Support

You'll need to hook up the monitor, the keyboard, the mouse and the old mini's TM backup drive to the new Mac before you turn it on to set it up (before the transfer).