Do you know what the user experience should be like?
Updated by Igor Goldobin 1 year ago. See history
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You should have a standard menu item "Check for Updates" in the Help menu. Here are a couple of examples of Check for Updates results:

❌ Figure: Bad example - Skype does a good job, with a green tick and simple message. The actual version number would have made it more complete

❌ Figure: Bad example - Snagit has horrible UI (red text when it is not an error and Hyperlinks without underlines), however the link to the latest features is not bad

✅ Figure: Good example - SSW Code Auditor has a great UI (using the freely available component in .NET Toolkit)
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If you implement this code from the SSW Toolkit, you will get this UI: