Sarah, welcome to the BVC family.
Does your theme have a right side column, that is... a content column 1, 2, 3? Adding a content block in a home page column is roll-off-the-wall easy.
Make a small graphic of the proper width (no wider than the column) and height (anything you wish). In the column of your choice, choose the 'HTML' content block and 'edit' into it (using the 'html' tab at the bottom of the edit box):
<A href="/category/Any category.aspx"><IMG alt="Your alt text" src="/images/Your image.jpg"></A>
'Any category' will be the category with the new or discounted products, 'alt' is the text that appears when you roll the mouse over the image (alt="Your alt text" is optional. Place some Google search terms here.), 'Your image.jpg' is the graphic you made in a Paint-type program and can be a jpg, bmp, gif, etc.
I highly recommend watching the videos here:
http://www.bvsoftware.com/bvcommerce5manual/http://www.bvsoftware.com/bvc2004/manual/Sorry if you know this already, but it seems to be what you're asking about.
It would help if you'd use a little more punctuation in your sentences.