From abroad, usually the best way to reach Chianti is to fly to an airport in Tuscany, such as the Pisa or Florence airport, or some other major airport in Italy. Alternatively, from Central Europe one might want to take a train to Italy. Once in Italy and preferably in Tuscany, you have to find your way to Florence; this will be easy as the city has good train connections to the rest of the country. From Florence there are several alternatives to get to Chianti: rental car, bus, taxi, etc.
Precise instructions are difficult to give since it depends so much on from where you are departing and exactly where you will be staying in Florence, in Siena, in Greve, or some other place in the region.