I have worked on a project to manipulate appointments (when I first started programming), and from VB, the easiest route to Exchange appointments at that time (avoiding MAPI) was using the Office Core & Outlook interop APIs named Interop.Microsoft.Office.Core.dll & Interop.Outlook.dll. As this was for an application on a desktop machine you needed to have Outlook installed on the same box, but this may have changed since (was around 4-5 years ago).
Alternatively with the the CDO libraries (which wrap the MAPI APIs), I don't think you need Outlook installed and these are relatively easy (and much faster) to use. May have been superceeded by now however.
Just on a side note, an application called OutlookSpy proved invaluable at the time for inspecting exchange runtime objects.