There are two ways to go about making a slideshow on your homepage. Both are in the Design section of your control panel under the content tab. This guide assumes that you're using a skin that supports slideshows, if you need to change to a design that support slideshows see How do I change my website theme?
The first option is to go to the "Images" tab of your website and add images to the "Image Gallery" option. This is a quick and simple to set up a slideshow but you do have limited control over the slideshow beyond simply controlling the images in it.
The second option is to go to the "Modules" tab of design and create a "Slideshow" promo module in Module Area 1, then adding images to that promo module. This can be more time consuming and complex than option 1 but gives you more flexibility to control things like the interval between photos changing and the look of the slideshow.