There are three options on how to get to Tbilisi center from Shota Rustaveli International Airport. There's the bus, the taxi and the train. The train is normally overlooked, in fact most arriving visitors don't even know that a train station exists at the airport even though the station building itself couldn't be any more noticeable. It one giant shinning golden globe.
Getting to Tbilisi
Most people arriving at Shota Rustaveli (Tbilisi) International Airport will either transfer to the city center by taxi or local bus. Local bus No.37 departs frequently from outside the main terminal building and costs just 0.50 GEL (0.20 US$). It takes around 45 minutes to Freedom Square / Liberty Square metro station and about a further 15 minutes to its last stop at the Main Railway Station. Along the way it passes a few metro stations but taking large suitcases on the metro is difficult if not even prohibited (I wouldn't know as a 35 litre rucksack is big enough for me).
The second option is to catch a taxi. It is much quicker at about 25 minutes but costs around 25 GEL (10 US$).
The third option, generally overlooked, is the train. Just 70 meters from the Airport Terminal is a train station that looks completely out of place. It is a striking piece of architecture, designed by the Georgian company "Delta-project 2000". The building entrance is dome shaped, clad with golden glass and in bright sunlight, the golden glass creates a yellow glow inside. To catch this train your flight needs to arrive (or depart) either in the morning or the late afternoon as there are only two daily trains from and to Tbilisi Main Station. If you do happen to have a perfectly timed flight, you will probably be the only tourist on the train.
The station platform at the Aiport is long enough for two carriages, however the train that operated along the route had five so my best advice is to try not to be in the back three carriages when departing Tbilisi. The first part of the journey from Tbilisi is relatively ok until the Airport line branches off from the main line. After this point the train speed becomes tediously slow.
From Tbilisi Main Station at 07:50 and 17:20 arriving at the Airport 35 minutes later.
From the Airport at 08:35 and 18:05 arriving Tbilisi Main Station 35 minutes later.
0.5 GEL (0.20 US$)
Georgian Railways - to access the train timetable first select English, then "Passenger Operations" on the right hand side. Then hover over "Traffic Schedule" and click on "Traffic General Schedule". This should open up a page with a list of all train services in Georgia, including the international trains to Yerevan (Armenia) and Baku (Azerbaijan).