Deployment
Out of the box TFS doesn't really support deployments, it can deploy to 1 location on build which often is a test server (think lab management). TFS 2012 has built in support for Azure deployments, but they still happen at the end of a build and the build artifacts cannot be automatically deployed to a new location.
You could modify the build template to allow to release to different locations, but that would still be a fresh build for every environment and not true binary promotions.
TFS does, however, have a concept of build quality and actually fires off events when this quality is changed. TFS Deployer is a 3rd party tool that hooks into the quality change event and can execute powershell scripts. This means with a simple change of a dropdown value you can automatically kickoff a script that releases to any environment you want. You can customize the build quality list (per team collection) to be a list of environments (dev, uat, staging, production etc) which the script then figures out where to release the specific build to.
VS2012 also has some nice improvements to web deploy which means deployment configurations are stored in source control with the project, which in theory means they'll be available in the drop folder for TFS Deployer to make use of.
I don't believe TFS keeps a history of build qualities, which means you can't really use the build quality history to maintain a list of what is deployed to which environment. You could fairly easily record this information as part of the deployment script though. Or at the very least add a custom summary node to the build with information about the release.
TFS2012 does have the ability to mark a build as deployed as part of the Azure deployment functionality, you mark tfs deployer builds as deployed using a script but it doesn't feel very useful.
Octopus Deploy is another project that's worth checking out, and could be used instead of TFS Deployer if your build template creates NuGet packages. It requires a bit more control over the production hardware as you need to install agents on each environment to handle releases, but it solves a lot of other issues with deployment.
Versioning
Once you have a nice consistent way of automatically releasing that people don't bypass, you can look at enhancing the build template to inject the build version, or changeset number as the assembly version for anything built as part of that automated build. There's a number of different ways to do it and plenty of blog posts and tools to help you achieve that.
Alternatively you could just use automatic assembly versioning ([assembly: AssemblyVersion("1.0.*")]) to give you the date/time the build occurred, which ends up like 1.0.1234.123 where 1234 is something like the days since jan 1st 2000, and 123 is the minutes since midnight (my specifics may be wrong here).
If you're deploying websites, then I highly recommend injecting the current build version into the html somewhere. This way you can check what version a website is running without needing access to the bin directory. It can also be appended as a querystring to css/js file imports to ensure no browser caching occurs between versions.
Thoughts
Personally I'm hoping Microsoft realise that the xaml build workflows are trying to do too much and that they split the different concerns (build, test, deployment...) into different scriptable parts. Of course that would not be until the next major release of TFS which is years away. Although with Team Foundation Service they are trying to iterate a lot quicker, so they may actually extend the Azure deployment stuff into something more useful in the nearer future.
