I am building an app in Xamarin Forms where you can buy products etc. Now I am at the stage where I want to send the user a confirmation when their order has been placed.
I have a string cointaining their email but I am not quite sure how to proceed. When I have previously worked with mail it looks something like this:
Device.OpenUri(new Uri("mailto:firstname.lastname@example.org?subject=free candy&body=you can trust me"));
You have a few options. If your email is a Microsoft Exchange mailbox, you can use Exchange Web Services (EWS), which is fairly simple if you follow code samples online. Otherwise, you should use an SMTP client. .NET has its own that you can include:
System.Net.Mail, or you can find a number of libraries online.
If you're inclined toward the .NET SMTP option, I would take a look at this question. It has a fairly complete example that should help you get started.
EDIT: You mentioned that your backend is PHP-Based. There are plenty of SMTP libraries for PHP as well and plenty of code samples. Here's another SO question I'd suggest you look at to help you get started in PHP instead of C#.