In your drop down component, select the Post Form on Value change.
In your Text box, make the Visible into a Process Defined, and use an Equals rule - when your Drop Down list variable name (it will be under This Form Data) equals Other, make it visible.
AS for validation, it's hard to do text box validation based on another variable, so I usually check the length of the text box after exiting the form. if the length is less than 2 or 3 characters, I redirect them back to the form and unhide an error box...
rob