At the moment the most sensible way to get to the centre appears to be via the WRO Airport Express shuttle bus, which runs every 50 minutes or so (with a break between 01:00 and 4:10) and will take you to the main train station with just one stop at Plac Dominikański on the way. The journey time is 30mins and the 10zł ticket can be purchased directly from the driver (cash or card). Alternatively, save a few złoty and go via bus 106, which runs roughly every 15mins between 05:14 and 23:30 from the airport to the main train station (Dworcowa stop), with central stops also at Pl. Orląt Lwowskich and Pl. Legionów. Night bus 206 departs the airport for the centre at 00:07, 00:37, 02:07, 03:36 (get off at 'Rogowska' and change to bus 241 going in the opposite direction), and 04:36 (change to 149 at 'Nowy Dwór'). However, the bus schedule is subject to change, so make it easy for yourself by using the website wroclaw.jakdojade.pl to plan your trip. Bus tickets cost 3.40zł and can be bought from the press store inside the terminal building or from the machine next to the bus stop. The journey takes 30-40mins.
If you prefer to go directly to your hotel doorstep, you can jump into one of the taxis sitting outside the terminal and expect a 20min ride to the centre. Pick-ups are restricted to a few vetted firms (but others are waiting nearby): currently Taxi Plus (tel. 601 711 058 or 602 647 555) and Partner Taxi (tel. 71 196 27). The tariffs are similar, but Partner Taxi seem to have the best rates: about 60zł weekdays, 70-80zł weekends.
For live arrival and departure information call the number given or visit the airport's excellent website.