i have just bought a new macbook air and i cant get it to connect to my hp deskjet f4580 printer. i have tried with usb and wireless. any ideas

The HP site has nothing new for that printer listed in HP Support.

They may (or not) show "AirPrint" download app in Mac app store.

As the printer appears to have been depreciated in a past macOS

an answer, would be to learn which new model best supports the

new Mac and its recent macOS. AirPrint shows nothing for it either.

Newer macOS does not support 32-bit drivers; a contributing factor

with Catalina/Big Sur '64-bit only' and demise to peripheral devices.

• About AirPrint - Apple Support

https://support.apple.com/en-us/HT201311

• 123.hp.com - Printer setup from HP Official Site

https://123.hp.com/us/en/

• HP Printers - macOS and OS X Compatible Printers | HP Support

https://support.hp.com/us-en/document/c01664444

• Official HP® Printer Drivers and Software Download | HP Support

https://support.hp.com/us-en/drivers/printers

• HP Printers - Printing with Apple AirPrint (iOS/macOS) | HP® Customer Support

You can look around, if you like. Just spent half hour there; &

sought information on "AirPrint" ~last gasp 'wi-fi' print effort.

(Better to look for newest model AIO or specialty printer that can

run the latest M1 Apple Silicon, or newest Intel-based Mac CPU)

• HP Deskjet F4580 All-in-One Printer Software and Driver Downloads | HP® Customer Support ...

https://support.hp.com/us-en/drivers/selfservice/HP-Deskjet-F4500-All-in-One-Printer-series/3944755/model/3944756

Obsoletism is the normal path for these semi-disposable items. Sorry!

🌞🌿⛵️🌤🎣🤖🏕🐝⛄️🌻🌎📫

You should be able to add it as an AirPrint printer in System Preferences > Printers & Scanners.

https://support.hp.com/us-en/document/c02623193