Most tourists arrive in Southern Armenia on a tour van. You can also arrange a private tour with guide with most companies, or just negotiate with taxi drivers in Yerevan to take you around. A taxi might be cheaper than renting a car, and easier than driving one.
Getting around in the South can be tough with public transportation, unless you're sticking to the main highway. From there, taxis or hitching are your best bets. On the main highway, buses and vans are frequent, and as long as they're heading in the right direction north/south it's tough to go wrong.
If you're not depending on public transport, just have wherever you are staying arrange a cab for you for the day. Taxis are reasonably priced in Armenia and usually can get you around for 100 drams 35 cents US a kilometer. There are no car rental agencies in the south, you can however rent a car in Yerevan and drive down.