Is it possible to transfer my current InDesign to a new computer? What is this procedure?
No... you do a fresh install
You install programs exactly the same way you did the 1st time... put your disc in the drive and enter your serial number when asked
Download & Install instructions https://forums.adobe.com/thread/2003339
-kglad links in reply #1 here https://forums.adobe.com/thread/2260248 will help
-you will need to enter your original serial number during install for non-Cloud programs
-download Lightroom https://helpx.adobe.com/lightroom/kb/lightroom-downloads.html
-Cloud Getting Started https://helpx.adobe.com/creative-cloud.html
-Membership questions and problems https://forums.adobe.com/thread/1146459
What version of InDesign? What operating system was the old machine? What operating system is the new machine?
And yes, it needs to be installed. There is no reliable way on Windows or Mac to migrate Adobe apps.