In order to craft a cake, you will need the following ingredients:
3 x wheat - this can either be obtained by harvesting some from a nearby village, or you can grow it yourself: find seeds by harvesting tall grass, and then use a hoe to till some ground and plant the seeds.
3 x milk - first, you will need to craft 3 buckets (from 3 iron ingots each) and then approach a cow until the "Milk" button appears. Press the button to fill the bucket with milk. You will get the empty buckets back once the cake has been made.
2 x sugar - this is made on a crafting table from sugar cane, the tall green stalked plant that grows along rivers.
1 x egg - this is a tricky one to get. Chickens in Minecraft seem to lay an egg once every 9-10 minutes, and this timer resets if you walk too far from the chicken. I resorted to following a chicken around for 9 minutes, and with a "plop" sound, it laid me an egg.
Take all these ingredients to the crafting table (not the furnace!) and you will be able to make the cake.