That cake looks like fun!
It looks like the top layer is just a frosted one-layer cake.
There are LOTS of different ways you could do this cake…. You could use a printed icing transfer sheet, you could ice the letters by hand, or you could use a stencil to paint the letters on. It just depends on what you have at hand, and what you think your skill level is. The printed icing sheet will be the easiest and cleanest. Call your local grocery store to see if they’ll print it out for you. Some places are very strict on trademarked logos, so you may have to find one that’s licensed. I think 9x11 is the biggest size they offer though. Then you can cut it to size, and just pipe some little decorations on the outer edges.
If printing is not an option for you, and you have access to a brush or airbrush, you can make a stencil. You can use clear acetate, or even thick card-stock. Find the logo, print it on regular paper, and then trace it onto your cardstock. Carefully cut out the letters using an x-acto knife. voila, stencil. Then place your stencil over your frosted cake (make sure it’s frozen or very cold so the icing is hard) and use your airbrush to paint on the surface. Alternatively, you could try using a smooth (preferably synthetic) brush and blue buttercream. Dip your brush in the buttercream, and try to run smooth strokes in the same direction over the letters. OR you could make your stencil and use sprinkles, or even edible glitter.
Otherwise you can do it by hand. Print out that Starwars logo on paper, put it on your cooled unfrosted cake, and cut the basic shape around it. After you cut the cake shape out, crumb coat the cake, let it cool in the fridge for a bit and then frost the cake smooth. Then put it back in the freezer until the frosting is very hard. Then, take your logo and carefully cut the letters out. Then, arrange the letters on your frozen cake and carefully, with a toothpick, outline the letters. You could either use a brush and paint inside the letters, then use a very fine tip and outline the letters in buttercream, or you can fill the letters with a star tip.
Hope this isn’t too confusing! Good luck!