Normally, there is no input control like a textbox available in Silverlight. You could use a HTML textbox and pass the value to Silverlight, but it would be cooler to create your own textbox and edit the style just like in WPF.
This is possible. A couple of days ago, I saw a presentation of Silverlight where some controls were developed by a Belgian company called Netika.
They showed a little trick to have keyboard input: trigger the KeyDown events and place them in a textblock. I started to create a tutorial for this and you can download the result below. The textbox is pretty basic, but of course you can make it look better using Expression Blend 2.0 September Preview and add some nice colors to it.
You can download the tutorial and the entire source code: