In Visual Studio 2010 select the Web Application project node in Solution Explorer then either:
Navigate to View -> Properties Window or press F4
Important: Don't Right-click -> Properties from the right-click context menu for the project node in solution explorer because that will show the Property Pages for the project which is a whole different thing.
In the properties Windows you'll see the entry for Managed Pipeline Mode:
In Visual Web Developer 2010 Express it's more or less the same, again select the web project except press F4 to get that property page:
The only caveat is that if you share the project with others (say via source control), this setting isn't stored in the .csproj file but in the IIS Express applicationHost.config file specific to your user profile. So you'd need to ensure others configured this property in their own local applicationHost.config files in:
All of the above also works with Visual Studio 2013 and 2015.