Select the text frame, and in the "Effects" panel, choose the "Drop Shadow" option at the bottom of the panel (it's the little "fx" icon). You'll get a dialog box which will allow you to adjust the shadow the way you want it. If you want it to affect just the text, make sure your text frame has a fill of "None".
Hope this helps,
I think I'd try adding the drop shadow as an attribute in the object style you use for your text frames.
The question seems unclear to me. Do you want to apply drop shadow to a whole text or a part of a text contained in a frame? because the second point is not possible. The drop shadow can only be applied to the whole text of a frame using the effect pannel (whatever the typografic formatting), I personnally create an object style and use a shortcut to apply it, or Quick Apply (ctrl/cmd + Enter+ds+ Enter ("ds" is the name of the my object style)).
You can apply a drop-shadow to the text directly even if the frame for the text has a fill colour, either by using the Effects Panel or the Object Effects button in the Control Strip (Illustrated here).
In the first instance, the text frame has no fill and the Drop Shadow option has been applied to the selected frame. In the second instance, the frame has a coloured fill and when the drop-shadow is selected by default it is applied to the fill of the frame. There is a drop-down at the top of the eefects panel enabling you to choose which particular attribute of an object the effect is applied to. In the third instance, the drop-shadow has been deselected for the object, and then applied to the text attribute.
well firstly: version ID?.