I have got a Imac macintosh. How do I go about upgrading it to a more recent operating system?

❗️ Do NOT upgrade until you have made a Time Machine or other backup of your startup drive.

Learn How to Back up your Mac with Time Machine

Your iMac (27-inch 2013) can run no newer macOS version than 10.15 Catalina.

Your current OS 10.9 Mavericks can be upgraded directly to Catalina if you like, or incrementally to Mojave 10.14.

I suggest you upgrade to Mojave first because any 32-bit apps you currently use now are not compatible with Catalina. Until you upgrade those app to their 64-bit versions or replace them with something else you shouldn't upgrade to Catalina.

How to Upgrade  macOS:

The macOS version you can upgrade to depends on the year your Mac was released.

Click the  (Apple) menu at the top of your screen and choose About This Mac.

Check the Compatibility of your Mac with newer versions of macOS:

➡️ macOS 10.14 Mojave is compatible with the Macs listed here

➡️ macOS 10.15 Catalina is compatible with the Macs listed here

❗️ – IMPORTANT – None of your 32-bit apps will work in Catalina.

https://support.apple.com/en-us/HT208436

Use the free utility Go64 to check the compatibility of your apps:

https://www.stclairsoft.com/Go64/

✅ - IF your Mac and apps are compatible, then using Safari only, download the macOS upgrade installer app:

Click > Mojave,  Catalina.

Once downloaded, double-click the “Install macOS…” app in the Applications folder to begin the upgrade.

• identify the model iMac you have (About This Mac)
• identify which MacOS you are currently running
• Identify which is the latest version for your IMac see link.

https://www.macworld.co.uk/feature/what-version-macos-compatible-3776008/

• if you can upgrade, later versions are found in App Store otherwise for earlier older versions see the link below.

https://support.apple.com/en-gb/HT211683

What help do you need? What model of iMac do you have? [Check out the "About This Mac" command in the apple menu on the left side of the menu bar]