Egg whites are easy enough. You can leave them covered in the fridge for up a week (great for macarons!) or freeze in individual ice cube trays. Make sure no yolks are caught up in the whites if you intend to whip them into a meringue – the fat from the yolk will prevent them whipping up properly.
Egg yolks are a bit trickier as they develop a skin on top if you store them whole. To save these, mix in either a tablespoon of sugar or a pinch of salt, then label and freeze.
Some uses for yolks; I love yolks so much more than whites! – ice cream, creme brulee, creme patisierre, creme anglaise, lemon or mango curd (use yolks for a richer curd), flan or my best ever peanut butter meringue buttercream