Did you just format your new hard drive? Or have you just wiped your computer clean? These are the steps I took to install Mojave, with my Bootable macOS Mojave USB Install Drive after installing and formatting my new hard drive.
Step 1.
Exit Disk Utility.
Step 2.
You should be taken back to the original menu, select Reinstall Mojave or OS.
Step 3.
Follow the prompts Apple provides to prepare you for software install.
Step 4.
Select your new Hard Drive.
Step 5.
Now you get to wait while your computer downloads and installs your new operating system. This will take some time.
Step 6.
Once your install is complete you will get to go ahead and set up your computer, following the same steps as you would if the computer were brand new and being set up for the first time. Except, now you are setting up a brand new hard drive for the first time.
Once your set up is complete, you get to enjoy your brand new hard drive and what seems like a brand new computer. It really is incredible how a new Hard Drive can make a seemingly failing computer, seem as if it were brand new. I really hope your installation is easy and enjoyable, and that you find pride in installing a new hard drive all on your own!