Flying to Trieste is simple enough, but with the wealth of airports and airlines to choose from finding the best Trieste flight can be rather harder.
If you're based in England then flying from London Stansted is probably your best option, as although you can get there from almost any international airport, flights from other airports tend to have one or more changes involved, adding to the price, journey time and hassle of the trip, so even if you live in the north of England it may still be better to travel to Stansted and then get a flight from there.
In terms of airlines, Ryanair currently seem to have the best offers, with flights between London Stansted and Trieste starting at roughly £60 for a return trip, and the flight time is only around two hours, so once you get to Stansted it's an easy journey the rest of the way.
However, while Ryanair's prices currently come out on top that may change at any time, so before booking it's always worth doing a price comparison with other airlines. There are several ways to do that, but the easiest is probably to go to fly.com, put in a search for flights to Trieste (although Trieste's airport is actually called Dei Legionari International, but putting in 'Trieste' will still find it) and see what it comes back with. The reason fly.com is recommended above any other comparison site is because many sites don't list Trieste or Dei Legionari International as a destination, making it impossible to run a comparison.