Yes, you should cover the styrofoam first.  You could paint it over with PVA but another method is to use masking tape, kept very smooth and only the best quality.
I would suggest not using pulp but laminating paper.  This way you can follow the contours very closely and have a surface that you can smooth with fine sandpaper.  Look through the articles on this site or get a book from the library to help you.  Look at the article 'What Paste to Use' and don't use boiled flour paste whatever you do.

One mistake beginners frequently make is to focus on applying the layers without taking the time to firmly smooth down each strip.

I can't emphasize enough the importance of this.  Lay a strip down, smooth firmly with your fingers, then use the top of your fingernail or the back of the bowl of a spoon, and burnish down any fold or ridge.  Only then should you apply your next strip.

If you rush through the job and leave the ridges and folds sticking up, they're going to make lumps, and applying more strips over them isn't going to help much. 

When the whole thing is dry, you will have a lumpy project.  Then you will have to sand it down until it's smooth.  Wait until you have to do it -- you won't realize how time-consuming it is!

Sue

Yes, nothing teaches the little ins and outs like actually doing it.

Sue