You should now have a mostly-assembled three-tiered wedding cake, although it's icing still looks a bit dodgy. You need to cover the crumb layer of icing with a smooth final layer of icing. To do this, start from the top of the cake and dollop some icing on the top, and on each of the horizontal tiers. Spread the icing into an even layer, covering all the tiers of the wedding cake.
Then, get a large class of warm to hot water, and a metal spatula. Dip the spatula in the warm water, then smooth over cake. Use the warm water frequently to help you remove any crevices or imperfections.
You can decide how "rustic" or "perfect" you want your cake to be. I was making this cake for a casual affair, so I appreciated the hominess of a cake made with hand-made love. If you're going for the smooth look, be aware that you'll never get it as smooth as cakes covered with fondant, but that fondant is not a good idea for beginners. If you want this cake without fondant to be very smooth, be prepared to spend an hour or so on this step.
A third option is to use a decorating triangle to add even ridges around the outside of the cake.