how can I upgrade my iMac 24-inch early 2008

Welcome to the Apple Support Communities.

Your iMac can only upgrade to OS X El Capitan. If you are not upgraded to OS X El Capitan, backup your files, and download it using Safari: How to get old versions of macOS - Apple Support. Finally, follow the instructions to run the installer.

Jack

Popular hardware upgrades including installing 4-6GB RAM and/or replacing the HDD with an SSD. You can find install videos at macsales.com

With that done El Capitan 10.11, the newest Apple supported version, will run smoothly... except that 10.11 is now starting to become dated itself. You might do better installing Mint Linux or saving up for a new iMac.

I would not spend any money on a 13 year old computer.It is no longer supported, has totally outdated hardware, and the hard drive will fail at some point. You will also be faced with the fact that a lot of websites will no longer support the old browser version(s) you are running.

Apple has a great refurbished section in their online store, so you can save some money on some older refurbished models.