Aer Lingus is the premiere airline traveling out of Ireland to a large selection of worldwide destinations. However, sitting for hours on end in economy seating may be dismal, since Aer Lingus is not known for its leg room.
Ask at the counter before you board your flight if you are able to upgrade. Usually, if you are, you will be asked to pay a nominal fee of $75-$100 US.
Wait and see if your flight is overbooked. Aer Lingus will usually offer you first class upgrades if you take a later flight than the one you initially planned so that other passengers may be accomodated.
Pay for it. This is the tried and true method. Call ahead of time and see if they will give you a special rate. You can also browse travel forums that give out special upgrade codes or are selling upgrades.
Call the airline and ask if you can buy a coach ticket with first class seating privileges. Sometimes you'll be able to get a first class seat for much less than the price.
Join Aer Lingus' Frequent Flyers program (The Gold Circle Club). If you earn enough points, you'll receive a complimentary upgrade to first or business class once or twice per year.