Tbilisi has excellent public transportation and it is very inexpensive. There are buses, the subway, and the ubiquitous mashrutkas. All of them charge about 25 cents.
The best and most convenient way to pay is to purchase a metro card at the window at the entrance to any subway station. The cards cost 3 lari and you can load them with as many lari as you like. I keep two cards with me and put about 20 lari on each so that when one runs out, I can easily switch and then reload the other one the next time I think about it. You can pay for any subway, bus or mashrutka with these cards and you don’t have to worry about having small change with you. To avoid embarrassment, do either keep a spare card charged or remember to keep your card topped up. It will take you a long time to go through 20 lari though.
The subway has two main lines, one north-south (roughly) and the other connecting to the north-south line about in the middle at Station Square (where Dezerter Bazaar is) and running east to Vazha-Pshavela. When you enter the subway station, pay attention to the sign as you exit the escalator. It will tell you which track (left or right) goes in which direction. You will need to memorize the four major endpoints: Station Square (west); Vazha-Pshavela (east); Akhmeteli Theater (north); and Varketili (south). They announce the direction points when the train arrives, first in Georgian and then in English. When you are on the subway, they announce the next stop, again in Georgian and English. You can only change lines at Station Square and there is clear signage in English to show you the way. The subway will get you most of the way to where you want to go, usually, but you will need to use a bus or mashrutka (or taxi) to get to some places.
The bus system is extensive and frequent. The bus stops are numerous and well-signed, many with electronic boards telling you which numbers stop there and when they are due to arrive. There is an app available for Android or IOS and you will save yourself some trouble by downloading it from the web site. You will find route maps, timetables and route planner. Just enter your origin and destination with the time you expect to leave and you will get a schedule with any connections.
Mashrutkas will get you everywhere, literally, but until you read Georgian fast enough, you should rely on a Georgian friend to help you. The mashrutkas are basically minivans with more comfortable seating than the buses for the same price. They stop ANYWHERE. All you have to do when you see one is wave it down and climb in. When you want out, you just say “ga-acheret.” You pay when you exit and you can use your card for this. At this time, there is no online route map to help you.
Lastly, you can take a taxi. Taxis are very inexpensive and the most you should pay for a trip “in town” is 8-10 lari (less than $3). However, BEWARE that you must negotiate the price and agree to it before you get in the taxi. And, many drivers speak absolutely no English or any other languages other than Georgian or Russian. A better option when you need a taxi is to download and use the Taxify app for Android or IOS. Then you can call for a taxi when you need it and the ride is automatically metered. You will pay no more than a street-hailed taxi and you will not have to bargain for the price. The downside to Taxify is that it will sometimes take several minutes (versus seconds to hail a taxi) before the taxi arrives.
In Tbilisi, it appears that literally anyone can drive a taxi, so you will often find that your driver doesn’t know where he’s going. If you use the Taxify app, you watch the cab coming for you in real time and often see the driver meandering the streets trying to figure out how to get to you. Many drivers have some sort of jerry-rigged GPS, but not all do. At least with Taxify, you can show him on your phone where he is going!
Always have the exact change when taking a taxi. Almost all drivers will claim that they have NO CHANGE whatsoever. Guard your one and two lari coins jealously so that you will not be in a spot so to speak.
A special note about taking a taxi from the airport:
There is a line of official airport taxis right as you exit the airport. USE THEM. ALL other drives will try very hard to cheat you. There are no exceptions to this rule. They will quote you a very high price (perhaps $30 US) and then if you only have two $20 bills, they will try to give you your change in laris (10 laris = less than $3). All flights arrive very late (after midnight), you will be tired and confused, and you might not pay attention until the next day. You will be unhappy then.
The fare from the airport should be no more than 30 laris (about $12 US). Of course, if you have to get laris from the ATM at the airport when you land, you are already in trouble because no one will have change for the large notes (or even the small ones), but the official taxis will try to find somewhere to make change on your way to your destination. No taxis will take credit cards of any kind.