I suppose that the majority of people reading this page and intending to visit Brno will travel there by air, landing at the city's Brno / Turany airport. I have to say, there are a lot worse airports to arrive or depart from, it is modern and rather pleasant and the major transportation hub for Southern Moravia.
Originally opened in 1958 as a joint military / civil aiport, it came under sole civil control as recently as 1992. The terminal building was built in 1986 and refurbished in 1996 and contains everything you would expect in a modern Western facility. I recall that the eating and drinking opportunities were good.
If you are interested in statistics, the runway is 2650 metres long, allowing it to handle Boeing 747's and passenger numbers topped half a million for the first time in 2008.
If you are arriving, there is a good bus service into the city and obviously taxis are available should you prever that option. See seperate tip for the details of the airport bus. A taxi into the centre should cost about 300 CZK ( 10 € ) and take about 20 minutes.
If you need to car, you have a choice of six rental agencies, including all the major ones.
Ryanair have a daily scheduled flight from London Stanstead airport direct to Brno which saves a transit stop. A taxi from Brno airport to either downtown or to the exhibition center is approx 10 Euro and takes about 20 mins.
There is also a main rail line going through the city with connections to Budapest, Moscow Vienna and of course to Prague.