Tbilisi Shota Rustaveli International Airport (TBS) is located 17 km southeast of Tbilisi and is served by taxis, buses and trains.
BUS
Municipality bus N37 serves passengers from Tbilisi International Airport to the Freedom Square and after Central Train Station. It’s the cheapest transportation and one way costs only 0.50 GEL. The journey takes about 30 - 40 minutes and they run every 20-30 minutes. Bus stop is located right in front of the Departure Hall and buses serve 24/7.
TAXI
Taxi service at Tbilisi International Airport is available outside the terminal. The journey time to the city center takes 20-30 minutes depending on the traffic. Taxis in Tbilisi are not metered, so you must negotiate before you get in the car. Expect to pay around 35 - 40 GEL.More info for the white taxis in front of the arrivals : Toyoto Taxi and Shuttle
Alternatively you can use Taxify application from your mobile phone.
TRAIN
There is a new train station serving Tbilisi Airport and conveniently dropping you at the main train station. The frequency, however, is disappointing, since it basically serves airport staff going to and returning from work.
Train Schedule Airport-Tbilisi: 8:35 am & 17:40 pm.
(The Georgian Railway train timetable can be found here. Do check train times before you travel as they may be subject to change.)