OK, so what I normally do is bake the cake beforehand (3 days for mud cake, 1-2 days for other cake) then once cooled smother it in glad wrap until it is air tight and freeze. It is easier to work with fondant on a frozen or part frozen cake. Then when it is decorating time I unwrap the cake and first use bits of fondant to fix any issues with the surface I.e. fill a hole with a blob, even up an uneven cake bottom bottom with a 'snake' of fondant along the low side etc. Then cover with butter cream smoothing it out with a palette knife, maybe even dampening the palette knife a couple times for extra smoothness. Then roll out the fondant and carefully place it over the cake. I haven't done an odd shape like that but I think I would try and roll the fondant as big as possible to give yourself lots to wrap around all the corners. First thing to do in gently smooth and rub the fondant over the cake with you very clean hands. The warmth of your hands warms the fondant a touch and gives it a bit extra 'give' when trying to shape it the cake. Keep very slowly working working it into shape until it looks like a sheet with a cake under it, then whip out the fondant smoother and smooth it even more. Then cut off the extra fondant and do the bottom edge however you want. You can cut it off and kind of poke the edge under but this can look a bit unfinished and lots of people put some other decoration over the top.

HTH