Basic cake recipe:
Put in a bowl (in this order)
6oz butter at room temp (ie soft)
6oz caster sugar
6oz self-raising flour
3 medium eggs
splash of vanilla extract
Mix together either with a wooden spoon or with mixer on slow setting until ingredients roughly combined, then beat hard (preferably with a mixer) until mixture is smooth and slightly paler. Maximum about 2 minutes with a good mixer.
Transfer to greased baking tin (about 8" should be fine, but smaller or larger not a problem as long as the mixture is no more than about 2" deep) and bake in the centre of a preheated oven at about 180C for about 30-45minutes. Do not open the oven until at least 30mins have passed. You can test the cake by either pressing the top gently with your finger (if it's ready the cake will bounce back, leaving no dent from your finger) or by sticking a long skewer into the middle of the cake (it's ready when the skewer comes out perfectly clean, or with just a few perfect crumbs on it).
Take out of oven, leave to cool for 5mins, then turn out and let finish cooling on a cake-rack. If you don't have a cakerack then a grill rack may do.
If you want, you can put the cake mixture into cupcake cases in a cupcake tray, in which case they will probably only take about 10mins to ccook. But keep an eye on them!
You can modify the cake by adding different extracts, eg orange oil, or spices, eg mixed spice, or chocolate drops, raisins, chopped nuts, etc. To make a nice chocolate cake, replace 1oz of the flour with cocoa powder (you must sieve it) and add a couple of tablespoonsful of chocolate drops or grated chocolate.
Have fun!