Normally on the web, a right mouse click makes a browser menu appear.
I am building a rich web application and most UI elements will have context menus with applicable actions on right click.
What would be the best way to let the user know that special functionality is available via a right click:
It depends on what the UI element is and in what context. If you're providing an element that normally has additional actions associated with it, by not having them readily present/visible the user will typically try to right-click/hover/etc. Once you establish that the right-click interaction exists on your application in one manner or another, the user will try it in other instances as well. That's basic recall.
If you want to see a good example of this, you can see that Gmail has a lot of right-click menus. They don't have a visual indication of the interaction either. You see that it works in one instance, subsequently driving you to attempt to use that particular interaction other instances. Take a look at the types of elements they utilize right-click for, as you will see a common theme in the type of menu items that accompanies them.
The best way to indicate this is to show it to a user in the First Time User Experience (say as a coach mark) and then assume it's a power-user-only feature – never again assume that they know that right click exists. This means duplicating functionality elsewhere to ensure that it's useful to everyone.
You could also reminder a user of the functionality with a tooltip or some help text. This is a helpful approach that doesn't assume the user remembers a special interaction to use some of your app.
Almost forgot cursor: context-menu; though that's infrequently used.
EDIT: Looks like the link from @Tory mostly covers my reasoning. There are a couple implementation ideas that add to that answer so I'm going to leave this up.
