How to use Azure Mobile Service API feature

And a couple more posts on this topic: http://blogs.msdn.com/b/carlosfigueira/archive/2013/06/14/custom-apis-in-azure-mobile-services.aspx (server side) and http://blogs.msdn.com/b/carlosfigueira/archive/2013/06/19/custom-api-in-azure-mobile-services-client-sdks.aspx (client side).

Also, since you tagged your question with ios, here's the code you'd use to call the API using an instance of the MSClient class:

If your API only deals with (receives / returns) JSON data:

MSClient *client = [MSClient clientWithApplicationURLString:@"https://your-service.azure-mobile.net"
                                             applicationKey:@"your-application-key"];
[client invokeApi:@"calculator/add"
             body:nil
       HTTPMethod:@"GET"
       parameters:@{@"x":@7, @"y":@8}  // sent as query-string parameters
          headers:nil
       completion:^(id result, NSURLResponse *response, NSError *error) {
    NSLog(@"Result: %@", result);
}];

Or with a request body (POST):

[client invokeApi:@"calculator/sub"
             body:@{@"x":@7, @"y":@8}   // serialized as JSON in the request body
       HTTPMethod:@"POST"
       parameters:nil
          headers:nil
       completion:^(id result, NSHTTPURLResponse *response, NSError *error) {
    NSLog(@"Result: %@", result);
}];

If your API deals with non-JSON data, you can use the other selector which takes / returns a NSData object:

NSData *image = [self loadImageFromSomePlace];
[client invokeApi:@"processImage"
             data:image
       HTTPMethod:@"POST"
       parameters:nil
          headers:nil
       completion:^(NSData *result, NSHTTPURLResponse *response, NSError *error) {
    NSLog(@"Result: %@", result);
}];