I dont know if the new Quark resepects alpha channels that will let you use a grayscale mask to designate different levels of transparency, but heres the basic way:
In photoshop, you will need to make a clipping path around the object. Its a vector-drawn outline of sorts that designates the boundries of the image. Once you have drawn your clipping path, you will need to name the path and designate it as a clipping path. When you re-save your tif file, you will be given the option to save the clipping path with it, which you'll want to say yes to. Once you place the image in quark, the option to mask the image to the clipping path is available in the options for the picture box. (be sure to set the background color of the box to NONE).
Newer versions of Quark might also give you the option to simply mask out all the white in a tif.
good luck!