I have an web application which runs on .net and is hosted in azure. We allow out clients to set reminders / alerts which then get emailed to them after they login.
How do we turn this into a real time service. IE: Automatically send the emails at the times set in the db. In the past I would have used a windows service, but I am not quite sure where to start looking at the moment.
I think what you want is to run the db-checking and emailing task in an Azure WebJob: Run Background tasks with WebJobs
With Azure Webjobs you could either make background tasks run on demand or at a set interval throug the websjob scheduler.
A few more links to get you started: