Main transport inside and outside the Tbilisi city is bus and minibus - marshrutka.
By Cab
Taxis in Tbilisi are typically privately owned vehicles, and don't run on a meter. If you're going anywhere other than the nearest metro station, major hotels, or tourist destinations, or if you don't speak Georgian or Russian, it's likely that your driver will stop multiple times and ask pedestrians for directions. Even then, he may not know how to get to your destination. If the driver has difficulty finding your destination, he will charge you for his trouble. ALWAYS negotiate a price beforehand, and insist on paying before departing. A trip anywhere in the city should never cost more than 10 lari, unless you're going to the airport.