Installing Mac OS

Which OS would you like, your question has very little content.

How to upgrade to macOS Mojave - Apple Support

How to upgrade to macOS High Sierra - Apple Support

How to upgrade to macOS Sierra - Apple Support

Before upgrading make a full back up of your Mac.

Check that third party apps you use have updates available for the new OS.

https://roaringapps.com

Check that your printers/ scanners etc have updated drivers and software available for the new OS.

Connect your mac to your router rather than rely on WiFi.

Do not use your mac while it is downloading

and do not use any other devices that share the same internet connection.

If you are considering upgrading to Catalina be warned that it does not support 32bit apps.

Your Mac is probably running 32bit apps and these will need to be updated to 64bit apps,

some updates may be free, some may be paid. Use this app to discover which apps you have

are 32bit, https://www.stclairsoft.com/Go64/. Once the list has been created you can then

contact the developers of the apps to see if they provide 64bit updates. 

How to upgrade to macOS Catalina – Apple Support

reinstall

How to reinstall macOS from macOS Recovery - Apple Support

If you are going to use the Recovery Servers you need to connect to your router via cable, do not rely on WiFi.

The certificates for several of Apples OS's expired in October 2019, Apple have been very poor at getting these updated on their Recovery Servers with valid certificates. This may be the problem you are experiencing. 

Try this workaround, we are going to set the time and date on your mac to a date previous to the expiry date of the certificates.

Make sure WiFi is switched off.

Boot to your Recovery HD, click on Utilities in the menubar select Terminal.

Enter a new date, for example or just copy and paste

sudo date -u 011421002016

press Return

enter your password

press Return

If Terminal returns an error saying sudo : command not found, then try again without sudo.

Now try downloading the OS.

If this works then when the OS is installed and booted up you can Open System Preferences> Date & Time

and reset the time back to today.