I will like to connect to sql express from visual studio. when I go to Database Explorer and click on add a new data connection I don’t get the option "Microsoft SQL Server".

I will like to connect to a SQL Server instance. Why does visual studio does not give me that option. I have installed sql express on this computer:

edit
Take a look how in this other computer I have more options:

It looks like this list is opulated based on installed DDEX (Data Designer Extensibility) providers. I am guessing here, but most likely your DDEX providers didn’t install correctly or somehow got uninstalled.
Did you try repairing your Visual Studio 2010 installation?