Make a cake similar to Victoria Sponge but that is moister (soured cream or buttermilk does the trick), so it will support the weight of the icing.
Here's a soured cream cake recipe to try:
85g unsalted butter, at room temperature, plus extra for greasing the dish
170g caster sugar
2 extra-large eggs, at room temperature
75ml sour cream
1/2 tsp grated lemon zest
1/2 tsp pure vanilla essence
150g plus 2 tbsps plain flour
1/2 tsp baking powder
1/4 tsp salt
1) Preheat the oven to 180C. Cream the 85g of butter and the remaining 170g of granulated sugar in the bowl of an electric mixer fitted with the paddle attachment, until light and fluffy. Lower the speed and beat in the eggs one at a time. Add the sour cream, zest and vanilla and mix until combined.
2) Sift together the flour, baking powder and salt and, with the mixer on low speed, add it to the butter mixture. Mix only until combined. Pour the cake batter evenly into two greased sandwich tins.
3) Bake for 30 to 40 minutes, until a cake tester comes out clean. Cool for 15 minutes, then invert the cake onto a flat plate.
With regards to icing, it can be easy.
First off, roll out the icing away from you on an icing-sugared surface to about 0.75cm-1cm thick (a good idea is to knead a tablespoon or so of vegetable shortening into the icing). Then, when it is rolled out to thickness and appropriate coverage, take the farthest end of icing and bring this over the rolling pin, so you are rolling it towards you.
Next, lubricate the cake by brushing it with some melted apricot jam (no bits please). Then, unroll the icing over the cake (a plastering trowel is good for smoothing over the cake to ensure there are no air bubbles - make sure this plastering trowel is not from your man's toolbox, please). Trim off any excess icing from the base of the cake.
Decorate as desired.