Hi,
Azure Monitor consists of several services. The question you are asking is very general so the reply will be such as well. Different resources emit logs and metrics. These logs and metrics can be send in third party by using diagnostic settings feature from Azure Monitor. The feature has the option to send the logs to Storage account, Event Hubs and Azure partner integrations. The last one is specific integration with specific third party tools. Event Hubs is also commonly used with third party tools by sending the data to Event Hub and from there the third party tool has some integration to collect them. Same is for Storage account but mostly Event Hubs is used. These two can also serve to write your own integration by pulling the data from them. Azure activity logs which are the Azure management plane logs can also be send via diagnostic settings. If you store data in Log Analytics (part of Azure Monitor) you can send the data from there to Storage Account or Event Hub for third party integration. Check the limitations as not all data can be sent. If you use any of the Azure Monitor alert types you can use action groups to integrate with third party systems. This could be things like ITSM tools. You will have to check if the third party tool provides some way to integrate with action groups. If not you can create your own integration by using automation tools like Azure automation, Azure Functions or Azure Logic app. You can even send the from the alert via action group data to a webhook. Assuming that the endpoint that receives the webhook will do some processing on its own to integrate with your third party. Whatever third party tool you use you should check with it what kind of integration offers with Azure Monitor. If it does not probably you will need to write your own integration and support it if you want to go that route.
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