Microsoft Silverlight and Adobe Flex are currently the 2 good options to make a rich client-web sevices app.

If you’re a .NET shop like us, you most likely have your web-services in C#. If you have a rich-client, it is most likely built in Flex/Flash. This is most likely market/business driven but also Flex has a decent model for building rich Internet clients consuming web-services and is platform independent (we’re not considering phones in this because Flex/Flash is no workie on many of them yet).

Although, Silverlight might take a while to reach a tipping point in the marketplace, the medium itself and related technologies have matured a lot and are quite compelling as a development platform, and would be my personal choice.
Silverlight definitely has the edge over Flex in terms of development, because it integrates tightly with the .NET IDE so you  have just one development platform and language which itself is a big win from a HR and team standpoint.

For development purposes, Microsoft has provided a framework called RIA (Rich Internet Application) Services that makes it easier to write a Silverlight Client that integrates with your web service.
I highly prefer the type integration it provides through library references instead of wsdl, which you would if developing with Flex.
Reflecting changes in web services (during development) seems to be a hassle with Flex Builder, if you regenerate from the wsdl and only need to copy over the new stuff if you want to do it selectively; I think a part of this hassle is our process/implementation.
A big hole in the strong typing via the proxy is that the proxy itself could be out of sync with the service, which does happen often during the development phase, and lead to runtime errors.

Apart from types being shared between the client and the server code, things like Validation rules are also shared, which is quite powerful.

This makes it a no-brainer to use Silverlight for Management Console/Support apps (because they are in-house and under your control) if you really want to go rich-client, while it might take some convincing of the business to use it for web apps, which honestly might be impossible as of now. 

Anyway, sticking to development, here is a quick overview of the various pieces involved in a RIA Services solution.

You use the Project – New – Silverlight Application template (like you always have for Silverlight projects). Following this, you will see the New Silverlight Application dialog.
It is important to check the box “Enable .NET RIA Services” at the bottom of the screen (which will show up only if you have RIA Services installed)
So, you will end up with a Solution containing 2 projects, viz. the Silverlight client with the RIA link enabled and the Website Server project.

Data model
Define your data classes with the ADO Entity Framework designer

This is the critical part, where you choose: Web Project – Add New Item – Domain Service class. Enter required details, which also let you choose Entities to manipulate, and you will end up with a class inheriting from the LinqToEntitiesDomainService of your Data Context class type.
The service class is decorated with: [EnableClientAccess()]  which exposes it to the client.
A Getxxx() method is generated to provide data.
Application logic should be added in/below the service class.

You can run the Project and see that the data entities are available in the client and server. This is an important distinction from writing a Flex client where there is no type sharing, and is a huge benefit for development.
This should not be confused with “no strong typing” – strong typing in Flex will be with proxy classes generated from the WSDL obtained by referencing your web service.

As mentioned earlier, type sharing is achieved by generating proxy classes in hidden code when you build the Project. The proxy classes include your DataContext, Entities, etc.
You can then access data from the Service by using a generic LoadOperation class which is in the System.Windows.Ria.Data namespace.

I have purposely kept this post at a high-level to get you started. There are a lot of details which I will delve into in future posts.

Some good resources are: