how do i install mac os on a new hard drive my old one quit

In Recovery, open Disk Utility.

From the View popup menu choose “Show All Devices”.

Select the new drive device (should be at top of list, outdented)

Click Erase button.

Select GUID Partition Map and APFS.

Name it and hit Apply.

Exit Disk Utility and choose Reinstall macOS or Restore from Time Machine.

It should go to Internet Recovery. Try holding down Cmd-Opt-R after you hear the startup tone (or when you power it on if yours doesn't have a tone).

It should go to Internet Recovery. Try holding down Cmd-Opt-R after you hear the startup tone (or when you power it on if yours doesn't have a tone).

About macOS Recovery on Intel-based Mac computers - Apple Support

I have the same problem after holding down option picking Wi-Fi for Internet recovery get screen for waiting for recovery or 15 minutes or so. then get a world with ! In the middle of it and Apple.com/support -5010U (1) . And sits there. Have to power down.

That means your connection to the internet is not robust enough to boot from Apple's servers.

You can try restarting modem and router, but you may have to take it to another network to access internet recovery.