There's a webhook option in the settings of the episerver form, so if you're pushing it to Azure I'd suggest just using that and posting it to Azure. You can post it direct to a webhook in Azure and then use an Azure function to process, although if you have not used logic apps I'd suggest looking at those as they are drag and drop logic builders that will take a webhook posts and with UI show you the data coming in and allow you to manipulate it or push it to another source (excel, google, dynamics, another web post, logic app). It's quite handy using logic apps as they are easier to edit and work with that Azure functions but either way I'd recommend the webhook.

The Episerver Service API has the ability to pull out submitted forms data too, so depending on your usecase - if you are happy to deal with these in batches this may be a useful alternative. https://world.episerver.com/documentation/developer-guides/Episerver-Service-API/episerver-forms-service-api/

I would agree that the easiest approach is using the webhooks. They can in turn call an Azure function, Microsoft Flow, Logic Apps or for example Zapier. I did a video a long time ago on how to easily setup a nice flow with Zapier and Episerver Forms:

https://www.youtube.com/watch?v=PZ7CSfCiqds&t=3s

Alf discusses the options here: https://talk.alfnilsson.se/2016/05/07/where-to-integrate-with-episerver-forms/ 

Depending on what you need to send over to your Azure function I'd go for a custom actor or look at using webhooks.

David