I have a cake recipe that needs three large eggs but what do I do if I only have medium eggs?
First we assume that you are referring to UK egg sizes as standard sizes do vary across countries. In the UK medium eggs are defined as those that weigh (still in their shells) between 53g and 63g and large are those that weigh between 63g and 73g. So if you have some scales handy then you may be able to pick out the larger eggs in the box and weigh them, then if they are at the top end of the medium weight range you should just be able to use them instead of large eggs.
If your medium eggs are on the small side then it will slightly depend on the recipe. If you are making a Victoria sponge then you can weigh the 3 eggs and just use the equivalent weight in butter, sugar and self-raising flour. However if the cake ingredients use other liquid ingredients, such as milk, you could use half of an extra beaten egg (approximately 1 1/2 tablespoons), though it is usually more practical just to separate an extra egg and add the yolk to the cake batter to make up the difference.
For the US the egg sizes are slightly different so a medium egg is defined as greater than 1.75 ounces, a large egg is defined as greater than 2 ounces and extra large as greater than 2.25 ounces. These sizes are smaller than the UK so a US extra large egg is actually the equivalent of a UK large egg. Nigella's recent US books mention using extra large eggs in the notes on the first couple of pages.
For Australia a medium egg is defined as 43g, a large egg as 52g and extra large egg as 60g. So an Australian extra large egg is the eqivalent to a UK large egg.