Travel

If you plan to arrive by plane, the local airport is Aeroporto FVG Ronchi dei Legionari (TRS).
Once you land at the Ronchi Airport, you can take the Bus #51 to Trieste Centrale (the bus depot alongside the train station); this should take about 55 minutes and costs ~4 Euro. The buses run until 11:30 pm (see timetable here). Warning: There is another Bus 51 that goes to Udine - do not take that one!.
If you prefer you can take a taxi from TRS airport to the city centre, though it is quite expensive (can be around 50-60 EUR). Usually, they are located just outside the main entrance. If you do not find one available, you can call one using a special phone close to the tourist office.

Alternatively, you could fly to Venice (Marco Polo) and take a half-hour bus (5 Euro) to Venezia-Mestre and then a 2-hr train (~11 Euro) to Trieste Centrale (you can look up the train timetable here). Warning: from the airport take the bus to Mestre, not Santa Lucia. Santa Lucia is the station for the main touristic area of Venice, while Mestre will provide the fastest connection to Trieste.

A cheap and convenient solution to go from Venice and Trieste airports to Trieste downtown is the "Science Bus". It is a shuttle service that provides direct transportation in a 8-seater mini bus to and from the nearest airports (including also Treviso and Ljubliana). You can find details about the service here.
Please note: who attends this workshop can ask to have a special discount for the Science Bus Service. If interested, write to Simonetta Fabrizio (fabrizio [at] oats.inaf.it) to have the code ("voucher number" on the Science Bus web site) that you have to use while booking the service on line. It costs ~15 EUR from Ronchi and ~88 EUR from Venice.

Getting around Trieste

You can walk across much of Trieste, although some areas are quite steep. Taxis are not too expensive; 10 Euros will get you from one end of town to the other. If you prefer to use public transportation, you need to buy a ticket at a "Tabacchi" (look for a big blue "T" sign) or at a newspaper kiosk. You can buy either a single ticket (~1 EUR) or a 10-trip ticket (~10 EUR). You need to stamp it once you get on the bus and this allows you to travel for 90 minutes and use mupliple buses. You can find more information about the buses here. Most of the buses run until 9pm, after which a few are replaced with the lines A, B, C and D. Ask local people for more detailed information

Getting the main University campus

To reach the main University campus you can take the bus 17/ at the terminal in front of the train station, or the bus 17 as indicated here in the map. In both cases, after ~10 mins, you have to get off the bus here (you'll see a parking on your right and a lawn in front of the main University building on your left - 350 meters after the petrol station there is the bus stop).
You might want to consider also buses number 3,4,39,51.

Reach the lecture room: the lecture room is 3B in the H3 building. Look at the map below (click on it for a larger version):



The following picture is the H3 building. Enter it, go to the third floor and look for "Aula 3B".