my old mac operating system needs reinstalling

Method 1: Create a USB installer (requires that your new Mac be capable of running a version of MacOS that will also run on the old Mac and/or that you have access to another old Mac) Create a bootable installer for macOS - Apple Support

Method 2: Internet Recovery: Use macOS Recovery on an Intel-based Mac - Apple Support

Assuming you purchased a new Mac that’s not possible. New Macs ship with the latest version of macOS and cannot be downgraded to an older one.

If you do not have a new Mac please advise of the model and year so we can determine what version of macOS will work with it.