As far as I know the cheapest flights to Malta are offered by Ryanair. They fly to Malta from London, Dublin, Bremen, Stockholm, Barcelona and Northern Italy. Usually if you book a flight in one month you can get prices between 20 euro and 100 euro, both directions (Maybe there will be a small increase of the prices in the summer, but in February I got there from Bremen for just 20 euros both waysincluding taxes) The prices depend on the weekday, usually flights on weekends are a little more expensive. Air Malta is the national airline company of Malta and I have heard that their flights are also not very expensive, but I don't have any experience with them.
If you are interested in sightseeing - Malta is wonderful during the winter - warm, sunny and not crowded with tourists. If you are interested in nightlife and beaches - the spring and the summer are the best seasons, in the winter there is almost no nightlife and the beaches are not so nice.
Good Luck with you journey

Ryanair is definitely a cheap option, but don't be fooled. The price they offer initially is complicated by taxes, fees for baggage (you pay per bag you check), and they are notorious for cancelling flights at the last minute. I have had several good experiences with Ryanair and several very bad ones as well. The website I use now is www.opodo.co.uk. They offer a wide range of affordable flights from the UK without all the extra charges.

I got a package holiday deal to Malta with Teletext holidays, it only cost £200- that included a return flight from London with three star hotel accommodation included and a travel guide with tours arranged for us. It was a good way to see Malta and a good price considering we went during the summer!

If you're flying from Europe I'd check www.seat24.com. This company searches travel agencies, special offers, and the airlines themselves and shows you a large selection of possibilities. I've had really good luck with them in the past. They also provide star ratings for travel companies and booking agents so you always know what you're getting into. Sometimes the fights are routed in strange ways, but they're quite a lot cheaper than direct flights.

I got a great deal from Air Malta that included return flights from London Gatwick, transfers and one week in an apartment with kitchen, twin room, bathroom, lounge, balcony, sea view, pool, shop and restaurant for £200